Package 'exams.forge'

Description

The exams.forge package was created with the main goal of "forging" exam tasks in combination with the exams package, and it includes additional functions to simplify the creation of Moodle exercises. The package features various functions categorized into seven groups based on their characteristics. These categories are named: Data Conversion and Modification, Statistical Analysis, Mathematical Computations, Exercise Generation, String Manipulation, LaTeX and HTML Functions, and General Purpose Functions.

Details

This package is designed for educators who need to develop examination materials in the field of statistics, particularly for introductory courses like Statistics I and II, using the R programming language. The aim is to streamline the process of creating a large number of assessment items, enabling instructors to focus on improving the quality of the tasks themselves.

We would like to acknowledge the support provided by the Multimedia Funding Program. Their assistance has been invaluable to our project, and we extend our sincere gratitude for their contributions.

Features of the package

• Feature 1: exams.forge simplifies the generation of examination tasks by providing tools to create a diverse array of statistical exercises, ensuring unique problem sets for each student.

• Feature 2: It includes functions for precise data conversion, statistical analysis, and mathematical computations, enhancing the accuracy and relevance of generated exercises.

• Feature 3: The package supports multi-format rendering, allowing the seamless creation of LaTeX and HTML documents suitable for various educational platforms, such as Moodle.

Functions

Examples of functions included in the package:

• ts_data: Creates a univariate time series by combining elements of a linear or exponential trend, additive or multiplicative seasonal adjustment, and white noise. The resulting time series is structured as a ⁠ts_data object⁠, allowing for further analysis and exploration.

• lmatrix: Creates a LaTeX or HTML representation of a matrix. This function is useful for integrating well-formatted matrices into LaTeX or HTML documents.

• as_obs: Creates a string representing observations with optional sorting and LaTeX formatting, useful for generating readable data representations in educational materials.

Usage

Example usage of the package and its functions.

library(exams.forge) # Generate a time series with specified parameters ts_eg <- ts_data(end = 20, trend = TRUE, trend.coeff = c(1, 0.5), season = TRUE, season.coeff = c(0.2, 0.1), error = TRUE, error.coeff = 0.1, digits = 2) print(ts_eg)

# Create a matrix mx_data <- matrix(1:6, ncol = 2) # Generate a LaTeX representation of the matrix with tooltip eg_matrix <- lmatrix( m = mx_data, title = "Example LaTeX Matrix", fmt = " byrow = TRUE, tooltip = "Die Tabelle hat cat(eg_matrix)

# Create a string representation of observations observations <- c(10, 20, 30, 40, 50) observation_string <- as_obs(observations, last = " and ") print(observation_string)

Installation

To install this package please use the following command: install.packages("exams.forge")

Author(s)

Sigbert Klinke, Affiliation: Humboldt University of Berlin, School of Business and Economics, Chair of Statistics.

Maintainer

Sigbert Klinke [email protected]

License

Gnu General Public License 3.

Author(s)

Maintainer: Sigbert Klinke [email protected]

Description

Adds data values to a given data vector x.

Usage

add_data(x, box, n = c(0, 1), range = c(0, 1))

Arguments

Details

Based on the data x, or the range(box), a box is computed. The length of the box gives the multiplier for the range. Then a left and right interval, from which the additional values are drawn uniformly, is computed: $[left box value-range[2]*box length; left box value-range[1]*box length]$ (left interval) and $[right box value+range[1]*box length; right box value+range[2]*box length]$ (right interval).

For box, "boxplot" can be also used and quantile(x, c(0.25, 0.75), na.rm=TRUE) can be used instead of range(x, na.rm=TRUE).

n can be a single number which will add n data values at the right side of x. If n is a vector of length two, then n[1] data values will be added at the left side of x and n[2] data values will be added at the right side of x.

Value

a data vector with new values

Examples

x <- rnorm(8)
# add one value to the right
add_data(x, "box", range=1.5)
add_data(x, "range", range=0.1)
add_data(x, "box", range=c(1.5, 3))
# add two values to the right
add_data(x, "range", n=2, range=0.1)
# add two values to the left and three to the right
add_data(x, "range", n=c(2,3), range=0.1)

Description

affix adds a prefix and/or a suffix to a (character) vector

math adds a $ as pre- and suffix to a (character) vector

bracket adds a ( as prefix and ) as suffix to a (character) vector

unaffix deletes a pre- and/or suffix to a (character) vector

unquote deletes double quotes at the beginning and the ending of a (character) vector

uncdata deletes a <![CDATA[ as prefix and ]]> as suffix

cdata adds a <![CDATA[ as prefix and ]]> as suffix

Usage

affix(txt, prefix = "", suffix = "")

math(txt)

bracket(txt)

unaffix(txt, prefix = "", suffix = "")

unquote(txt)

uncdata(txt)

cdata(txt)

add_affix(txt, prefix = "", suffix = "")

add_cdata(txt)

add_math(txt)

lmath(txt)

add_bracket(txt)

brkt(txt)

remove_affix(txt, prefix = "", suffix = "")

remove_quotes(txt)

remove_cdata(txt)

Arguments

Value

a character vector

Examples

x <- runif(5)
affix(x, "$", "$")
math(x)

Description

Tests if the differences between the entries in obj are larger than tol.

Usage

all_different(obj, tol)

Arguments

Value

logical

Examples

x <- runif(10)
all_different(x, 0.0001)
all_different(x, 1)

Description

Rounds x according to digits, FUN and sets a tolerance for the result. If the tolerance is not stated, consider it the maximum of 2*10^(-digits).

Usage

as_result(x, digits, tol = NA, FUN = round2)

tol(x)

rounded(x)

val(x)

digits(x)

as_res(x, digits, tol = NA, FUN = round2)

tolerance(x)

Arguments

Value

A list with the original and a rounded value, digits used and tolerance.

Examples

x <- as_result(1/3, "prob")
tol(x)
rounded(x)
tol(x)
digits(x)

Description

Converts a character vector into a single string.

Usage

as_string(txt, collapse = ", ", last = ", and ")

as_sum(txt)

as_obs(txt, name = "x", sorted = FALSE, ...)

as_fraction(val, latex = FALSE, sorted = FALSE, ...)

lobs(txt, name = "x", sorted = FALSE, ...)

lstring(txt, collapse = ", ", last = ", and ")

lfrac(val, latex = FALSE, sorted = FALSE, ...)

Arguments

Value

a string

Examples

x <- runif(5)
y <- c(TRUE, FALSE, NA) 
as_string(x)
as_string(y)
# toString
as_string(as.character(x))
as_string(as.character(y))
#
as_obs(x)
as_obs(sort(x), sorted=TRUE)
#
x <- round(runif(5), 2)
as_fraction(x)
as_fraction(x, TRUE)
#
y <- round(runif(5), 2)
as_sum(x)

Description

Converts a vector into a horizontal table.

Usage

as_table(
  x,
  caption = NULL,
  label = NULL,
  align = NULL,
  digits = NULL,
  display = NULL,
  auto = FALSE,
  ...
)

toTable(
  x,
  caption = NULL,
  label = NULL,
  align = NULL,
  digits = NULL,
  display = NULL,
  auto = FALSE,
  ...
)

Arguments

Value

A string.

Examples

x <- runif(5)
tab <- vec2mat(x, colnames=1:length(x))
as_table(tab)

Description

Converts a ts_data object into a time series object (ts).

Usage

as_ts(ts)

Arguments

Value

A ts object.

Examples

# Time series from linear trend
ts <- ts_data(12, trend.coeff= c(sample(0:10, 1), sample(1+(1:10)/20, 1)))
as_ts(ts)

Description

Given a frequency table, the function reorders the observations such that the given target association will be approximated and the marginal frequencies remain unchanged. Note that the target association may not be reached! zero allows for zero entries in the common distribution. If target is NA then the table is simply returned. FUN computes the association (or correlation) measure based on a frequency table. tol gives the maximal deviation of the association (or correlation) measure and the target value. maxit limits the number of steps. Please note that a solution is not guaranteed, especially for extreme values of target, for example for $+1$, $-1$ or nearby values. If attr(joint, "iterations")== maxit then you need either to increase maxit, to decrease tol, or check if you have chosen an appropriate target value (for a nominal measure in $0 <= target <= 1$, for ordinal measure in $-1 <= target <= +1$). attr(joint, "target") contains the achieved association.

Usage

assoc_data(
  tab,
  zero = FALSE,
  FUN = nom.cc,
  target = NA,
  tol = 0.001,
  maxit = 500,
  ...
)

reorder_association_data(
  tab,
  zero = FALSE,
  FUN = nom.cc,
  target = NA,
  tol = 0.001,
  maxit = 500,
  ...
)

dassoc(
  tab,
  zero = FALSE,
  FUN = nom.cc,
  target = NA,
  tol = 0.001,
  maxit = 500,
  ...
)

Arguments

Value

a modified frequency table

Examples

tab <- table_data(3, 2)
tab
tab2 <- assoc_data(tab, target=0.5)
tab2

Description

Generates a data frame with potential values for size and prob, and is subjected to specific conditions:

• If length(mean) == 1 and it's an integer, it signifies the desired number of digits for the mean.

• If mean is set to NA (the default), all means are permissible.

• When length(mean) > 1, the product size * prob must be one of the valid means.

• The same rules applies to sd.

The parameters norm and pois can take on values of NA, TRUE, FALSE, or be defined as a function in the format: ⁠function(size, prob)⁠. These values determine which ⁠(size, prob)⁠ combinations are eligible:

• For NA, all combinations of ⁠(size, prob)⁠ are acceptable.

• If specified as a function, only those combinations for which the function returns TRUE are considered valid.

• If set to TRUE, combinations are accepted only if they satisfy either the condition size * prob * (1 - prob) > 9 (for norm, indicating a normal distribution approximation), or the conditions prob < 0.05 and n > 10 (for pois, implying a Poisson distribution approximation).

• If set to FALSE, the approximations should not hold for any combination.

Please be aware that there is no guarantee that the resulting data frame will include a valid solution.

Usage

binom_param(n, p, mean = NA, sd = NA, norm = NA, pois = NA, tol = 1e-06)

Arguments

Value

a data frame with possible choices of n , p, mean and sd

Examples

binom_param(1000:50000, (5:25)/100, 0, 0)

Description

Creates a number of equidistant or non-equidistant breaks for given data x. If width is not given then it will be set to diff(pretty(x))[1]. probs can either be a single integer, giving the number of quantiles, or a vector of probabilities with values in $[0,1]$. Please note that if width is too large, then using probs may result in equidistant breaks too.

Usage

breaks(x, width = NULL, probs = NULL)

add_breaks(x, width = NULL, probs = NULL)

dbreaks(x, width = NULL, probs = NULL)

Arguments

Value

A numeric vector of breaks.

Examples

x <- rnorm(100, mean=1.8, sd=0.1)
breaks(x)
breaks(x, 0.1)
breaks(x, 0.1, probs=4)

Description

Checks if the result from base::sys.calls contains a call from fun.

Usage

calledBy(fun = "exams2pdf")

called_by(fun = "exams2pdf")

Arguments

Value

logical

Examples

funb <- function() { calledBy('funa') }
funa <- function() { funb() }
funa()

Description

Calls cat if cond==TRUE.

Usage

catif(cond, ...)

condition_cat(cond, ...)

Arguments

Value

Invisibly cond.

Examples

catif(TRUE, "PDF")      # Should appear
catif(FALSE, "Moodle")  # Should not appear

Description

The CImu_data function is designed for the generation of confidence intervals pertaining to a population mean mu. The function accommodates scenarios in which a dataset x is either provided or generated through a random sampling process from a normal distribution, with user-specified parameters such as a mean mu and a standard deviation sigma. Subsequently, the function computes essential statistical measures, including the sample mean xbar and the standard deviation sd. Confidence intervals for the population mean are then calculated at user-defined confidence levels (conf.level). The output is a structured list containing pertinent statistics, encompassing the mean, sample standard deviation, confidence intervals, and other relevant details.

Usage

CImu_data(
  x = NULL,
  n = length(x),
  xbar = NULL,
  sd = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  mu = NULL,
  sigma = NULL
)

dcimu(
  x = NULL,
  n = length(x),
  xbar = NULL,
  sd = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  mu = NULL,
  sigma = NULL
)

Arguments

Value

a list with

• a with 1-(1-conf.level)/2

• n number observations if given

• xbar mean of observations if not given

• mu theoretical mean if given

• sd standard deviation of observations

• sigma theoretical standard deviation if given

• df degrees of freedom if a t distribution is used

• q if sigma=NULL

• ss either sd or sigma

• e margin of error (half of the length of the confidence interval(s))

• l length of the confidence interval(s)

• v endpoints of the confidence interval(s)

Examples

# with data
x <- rnorm(100)
CImu_data(x, conf.level=0.95)
# simulate data internally
CImu_data(n=100, conf.level=0.95, mu=0, sigma=1)

Description

Data generation for the necessary sample size of a confidence interval, for the population mean value. Either the estimation error $e$ or the length of the interval $l$ must be given ($l=2*e$). It is ensured that the computed s deviates from sigma.

Usage

CImulen_data(
  sigma,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

dcimulen(
  sigma,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

Arguments

Value

A data frame or a list with:

• $e$: estimation error

• sigma: population variance

• conf.level: confidence level

• $l$: interval length

• x: $1-alpha/2$

• q: $z_{1-alpha/2}$

• q2: $z^2_{1-alpha/2}$

• n: computed minimal sample size

• N: the smallest integer, no less than n

• s: sample standard deviation

Examples

# one solution
CImulen_data (1:10, e=(1:10)/10)
# all solutions
mul <- CImulen_data (1:10, e=(1:10)/10, full=TRUE)
str(mul)

Description

Data generation for the necessary sample size of a confidence interval, for the population proportion, using $z^2/l^2)$. Either the estimation error $e$ or the length of the interval $l$ must be given ($l=2*e$). It is ensured that the computed p deviates from pi.

Usage

CIpilen_data(
  pi,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

dcipilen(
  pi,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

Arguments

Value

A data frame or a list with:

• $e$ estimation error

• pi population proportion

• conf.level confidence level

• $l$ interval length

• x $1-alpha/2$

• q $z_{1-alpha/2}$

• q2 $z^2_{1-alpha/2}$

• n computed minimal sample size

• N the smallest integer, no less than n

• p sample proportion

Examples

# one solution
CIpilen_data((1:9/10), (1:9)/10)
# all solutions
pil <- CIpilen_data((1:9/10), (1:9)/10, full=TRUE)
str(pil)

Description

• permutation computes the number of permutations

• variation computes the number of variations with and without replication

• combination computes the number of combinations with and without replication

• combinatorics computes all combinatorics results for k < n and returns it as list of:

  permutation.n

  $P(n)$

  permutation.k

  $P(k)$

  permutation.nk

  $P(n; k)$

  variation

  $V(n;k)$

  variation.rep

  $V^W(n;k)$

  combination

  $K(n;k)$

  combination.rep

  $K^W(n;k)$

• lfact computes the natural logarithm of the factorial of a given number n

• lfactquot calculates the natural logarithm of the quotient of factorials

• lbinom computes the natural logarithm of the binomial coefficient, "n choose k"

Usage

combinatorics(n, k)

variation(n, k, repl = FALSE)

combination(n, k, repl = FALSE)

permutation(n, k = rep(1, n))

lfact(n)

lfactquot(n, ...)

lbinom(n, k)

combo(n, k, repl = FALSE)

combs(n, k)

fact(n)

factquot(n, ...)

binom(n, k)

Arguments

Value

A list.

Examples

permutation(8)
permutation(8, c(1,3,2,2))
combination(8, 4)
combination(8, 4, TRUE)
variation(8, 4)
variation(8, 4, TRUE)
combinatorics(8, 4)

Description

Generates a data set based on x and y for a given target correlation r according to stats::cor(). The algorithm modifies the order of the y's, therefore is guaranteed that the (marginal) distribution of x and y will not be modified. Please note that it is not guaranteed that the final correlation will be the desired correlation; the algorithm interactively modifies the order. If you are unsatisfied with the result, it might help to increase maxit.

Usage

cor_data(
  x,
  y,
  r,
  method = c("pearson", "kendall", "spearman"),
  ...,
  maxit = 1000
)

dcorr(x, y, r, method = c("pearson", "kendall", "spearman"), ..., maxit = 1000)

Arguments

Value

A matrix with two columns and an attribute interim for intermediate values as matrix. The rows of the matrix contain:

• if method=="pearson": $x_i$, $y_i$, $x_i-bar{x}$, $y_i-\bar{y}$, $(x_i-bar{x})^2$, $(y_i-\bar{y})^2$, and $(x_i-bar{x})((y_i-\bar{y})$.

• if method=="kendall":

  • $x_i$: The original x values.

  • $y_i$: The original y values.

  • $p_i$: The number of concordant pairs.

  • $q_i$: The number of discordant pairs.

• if method=="spearman": $x_i$, $y_i$, $p_i$ (concordant pairs), and $q_i$ (disconcordant pairs). In a final step a vector with the row sums is appended as further column.

Examples

x <- runif(6)
y <- runif(6)
xy <- cor_data(x, y, r=0.6)
cbind(x, y, xy)

Description

Generates a sequence of sample sizes in a range from min=5 to a max:

• whose root is an integer (data_nsq), and

• that are divisible only by 2 and 5 (data_n25)

Usage

data_n(max, min = 5)

data_nsq(max, min = 5)

data_n25(max, min = 5)

dn(max, min = 5)

dn25(max, min = 5)

dnsq(max, min = 5)

Arguments

Value

A sequence of integers.

Examples

data_n(10)
data_nsq(1000)
data_n25(1000)

Description

Generates a nrow × ncol matrix with probabilities / frequencies. If data is given it will be normalized such that sum(data[is.finite(data)])==1. If no rownames or colnames are given then event names from LETTERS are used. The returned matrix will have the following attributes:

• marginals a list of the row and column marginal distributions

• byrow a matrix with conditional probabilities by row

• bycol a matrix with conditional probabilities by column

• expected a matrix with the expected probabilities under independence

• prob a vector of all the probabilities computed (except the expected ones)

Usage

data_prob2(
  data = NULL,
  nrow = 2,
  ncol = 2,
  colnames = NULL,
  rownames = NULL,
  ...
)

prob_mx(data = NULL, nrow = 2, ncol = 2, colnames = NULL, rownames = NULL, ...)

dprob2(data = NULL, nrow = 2, ncol = 2, colnames = NULL, rownames = NULL, ...)

Arguments

Value

A matrix and some attributes.

Examples

x <- data_prob2()
str(x)
data_prob2(colnames="E")
data_prob2(nrow=3)

Description

Creates a discrete probability function based on x with a resolution unit. If unit is not given then unit will be 10, 100, 1000, ... depending on the length of the discrete probability function.

Usage

ddiscrete(x, unit = NULL, zero = FALSE)

Arguments

Value

A discrete probability function.

Examples

ddiscrete(runif(6))
ddiscrete(6)
ddiscrete(6, 20)
ddiscrete(c(1,0,0,0), zero=TRUE)

Description

Creates a bivariate discrete probability function based on the marginal probability functions row and col. If unit is not given then unit will be the product of the units used in row and col, otherwise it will appear as the least common multiple unit product of the units used in row and col. If target is NA then the common distribution of two independent random variables is returned, otherwise an iterative algorithm is run to approach a target association or correlation measure, see also assoc_data() (called internally). zero allows for zero entries in the common distribution. FUN computes the association or correlation measures based on a frequency table. tol gives the maximal deviation of the association or correlation measure and the target value. maxit limits the number of steps. Please note that a solution is not guaranteed, especially for extreme values for target, for example for $+1$, $-1$ or nearby values. If attr(joint, "iterations")==maxit then you need either to increase maxit, to decrease tol or to check if you have chosen an appropriate target value (for a nominal measure in $0 <= target <= 1$, for ordinal measure in $-1 <= target <= +1$).

Usage

ddiscrete2(
  row,
  col,
  unit = NULL,
  zero = FALSE,
  FUN = nom.cc,
  target = NA,
  tol = 0.001,
  maxit = 500,
  ...
)

biv_discrete_prob(
  row,
  col,
  unit = NULL,
  zero = FALSE,
  FUN = nom.cc,
  target = NA,
  tol = 0.001,
  maxit = 500,
  ...
)

Arguments

Value

A bivariate discrete probability function.

Examples

row <- ddiscrete(runif(5))
col <- ddiscrete(runif(3))
joint <- ddiscrete2(row, col)
joint
joint <- ddiscrete2(row, col, target=0.5)
joint
nom.cc(joint*attr(joint, "unit"))

Description

Probability mass function, distribution function, quantile function and random generation for the sum of two independent discrete uniform distributions.

Usage

ddunif2(x, min = 1, max = 6)

pdunif2(q, min = 1, max = 6)

qdunif2(p, min = 1, max = 6)

rdunif2(n, min = 1, max = 6)

sum_discrete_unif_cdf(x, min = 1, max = 6)

sum_discrete_unif_pmf(q, min = 1, max = 6)

sum_discrete_unif_quantile(p, min = 1, max = 6)

sum_discrete_unif_rand(n, min = 1, max = 6)

Arguments

Value

A numeric vector with the same length as x.

Examples

ddunif2(1:13)
pdunif2(1:13)
qdunif2((0:4)/4)
rdunif2(10)

Description

Holds an univariate distribution including its parameters. The name of the distribution is used to determine the right use of the function. For example, in the case of function for quantiles: paste0("q", name). Usually the full name has to be used; some abbreviated names are possible:

• binom binomial distribution, parameters: size, prob

• hyper hypergeometric distribution, parameters: m, n, k

• geom geometric distribution, parameters: prob

• pois Poisson distribution, parameters: lambda

• unif continuous uniform distribution, parameters: min, max

• dunif discrete uniform distribution, parameters: min, max

• dunif2 continuous uniform distribution, parameters: min, max

• exp exponential distribution, parameter: rate

• norm normal distribution, parameters: mean, sd

• lnorm log-normal distribution, parameters: meanlog, sdlog

• t Student t distribution, parameter: df

• chisq chi-squared distribution, parameter: df

• f F distribution, parameters: df1, df2

Note that a probability mass/density, quantile and a cumulative distribution function must exist.

The following functions exists for disributions:

• distribution creates a distribution with name and parameters

• quantile computes the quantiles of a distribution using paste0('q', name)

• cdf computes the cumulative distribution function of a distribution using paste0('p', name)

• pmdf computes the probability mass/density function of a distribution using paste0('d', name)

• prob computes the probability for a interval between min and max (max included, min excluded)

• prob1 computes the point probability f

• is.distribution checks if object is distribution object. If name is given then it checks whether the distribution type is the same

• toLatex generates a LaTeX representation of the distribution an its parameter

Usage

distribution(name, ...)

## Default S3 method:
distribution(name, ..., discrete = NA)

## S3 method for class 'distribution'
quantile(x, probs = seq(0, 1, 0.25), ...)

cdf(x, q, ...)

## S3 method for class 'distribution'
print(x, ...)

## S3 method for class 'distribution'
summary(object, ...)

pmdf(d, x, ...)

## S3 method for class 'distribution'
toLatex(object, name = NULL, param = NULL, digits = 4, ...)

is.distribution(object, name = NULL)

prob(d, min = -Inf, max = +Inf, tol = 1e-06)

prob1(d, x, tol = 1e-06)

compute_cdf(x, q, ...)

compute_pmdf(d, x, ...)

compute_probability(d, min = -Inf, max = +Inf, tol = 1e-06)

point_probability(d, x, tol = 1e-06)

pprob(d, x, tol = 1e-06)

is_distribution(object, name = NULL)

Arguments

Value

A distribution object.

Examples

d <- distribution("norm", mean=0, sd=1)
quantile(d)
quantile(d, c(0.025, 0.975))
cdf(d, 0)
is.distribution(d)
is.distribution(d, "t")
toLatex(d)

Description

A data frame with the R function names, LaTeX names, discreteness and package origin of a distribution.

Usage

data(distributions)

Format

A data frame with columns r, latex, discret and package

Examples

data(distributions)
distributions

Description

• is_terminal checks whether x's can be expressed as a terminal fraction, basically divisor_25(denominator(x))

• divisor_25 checks whether all x's can be expressed as $2^x 5^y$

• prime_numbers returns all prime numbers up to a limit

• primes prime factorization of x, returns a matrix with the power of each prime number

• has_digits checks whether the x's have only digits after the decimal point, basically abs(x-round(x, digits))<tol

• all_integer checks whether all x's are integer, basically all(has_digits(x,0))

Usage

divisor_25(x)

denominator_25(x)

is_terminal(x)

round_25(x)

prime_numbers(n, sieve = FALSE)

primes(x, min = 2)

has_digits(
  x,
  digits = 2,
  tol = 10^{
     -digits - 6
 }
)

all_integer(x)

only_digits(
  x,
  digits = 2,
  tol = 10^{
     -digits - 6
 }
)

is_term(x)

denom_25(x)

Arguments

Value

logical

Examples

is_terminal(2/3)   # 0.6666... non-terminal
is_terminal(1/5)   # 0.2       terminal
divisor_25(1:25)
prime_numbers(100) # all prime numbers less equal 100
primes(1:20)       # prime factorization of 1 to twenty

Description

It performs a comparison by checking if either abs(x - y) < tol when outer == FALSE, or if an a exists or a y[j] for each x[i] such that the condition abs(x[i] - y[j]) < tol is satisfied.

Usage

equal(x, y, tol = 1e-06, outer = FALSE)

approx_equal(x, y, tol = 1e-06, outer = FALSE)

Arguments

Value

logical

Examples

equal(9*1/9, 1)

Description

equations defines a set of equations using the formula interface including a LaTeX representation of the formulae.

variables sets the variable values, the LaTeX representation and the solution interval. The first argument must be the equations object. A named parameter starts the setting for a specific variable, e.g. ⁠..., s=1, pos(5), "s^2",...⁠ sets for the variable s first its numerical value, second the solution interval and finally the LaTeX representation.

Usage

equations(...)

variables(...)

Arguments

Value

(for equations) An equations object.

(for variables) The modified equations object.

Examples

# The equations describe the formulae for an confidence interval of the mean
e <- equations(o~x+c*s/sqrt(n), "v_o=\\bar{x}+c\\cdot\\frac{s^2}{n}", 
               u~x-c*s/sqrt(n), "v_u=\\bar{x}-c\\cdot\\frac{s^2}{n}", 
               e~c*s/sqrt(n),   "e  =c\\cdot\\frac{s^2}{\\sqrt{n}}",
               l~2*e,           "l  =2\\cdot e"                   
               )
print(e)
e <- variables(e, 
               x=0,    "\\bar{x}",
               c=2.58, dbl(2), 
               s=1,    pos(5), "s^2",
               n=25,   pos(5),
               l=pos(5), 
               e=pos(5),
               u="v_u", o="v_o")
print(e)

Description

Returns a list with the functions' names and parameters called from .traceback(). The function name must start with "exams2".

Usage

exams2call(prefix = "exams2")

Arguments

Value

A list with the function name and its valuated parameters.

Examples

exams2call()                 # access current call stack

Description

Data structure for exercise data.

Usage

exercise(exer, ...)

## Default S3 method:
exercise(exer = NULL, ...)

exercise_data(exer, ...)

Arguments

Value

An exercise object.

Examples

exer <- exercise()           # new exercise
exer <- exercise(exer, x=3)  # add x to the exercise

Description

Computes the real valued extremes (minima, maxima, and saddle points) for a univariate polynomial. The computation can be limited to a specific type of extremes.

Usage

extremes(p, type = c("all", "minimum", "maximum", "saddle"), tol = 1e-09)

Arguments

Value

A numeric vector.

Examples

p <- polynomial(c(0,0,0,1))
extremes(p)
p <- integral(poly.calc(-1:1))
extremes(p)

Description

Converts a number to a string containing either a floating point or a fractional number. Note that a repeating or recurring decimal, which is a number whose decimal representation becomes periodic, can also be expressed as a rational number. For example, $\frac{1}{3}=0.333333333...=0.\overline{3}$. It is the workhorse used in num2str.

• If denom is negative then always decimal point numbers are used (default).

• If denom is zero then a mix of decimal point and fractional numbers are used (whatever is shorter).

• If denom is one then fractional numbers are used except for integers.

• If denom is larger than one, then the denominator is set to denom if possible.

Usage

fcvt(x, nsmall = 15, plus = FALSE, denom = -1)

Arguments

Value

A character.

Examples

x1 <- c(NA, NaN, -Inf, Inf, 0, pi*10^(-20:20))
fcvt(x1)
x2 <- c(-0.36, 3.6, -30.6, 0.36)
fcvt(x2)
x3 <- c((0:16)/8, 1/3)
fcvt(x3)           # as floating point number, equals denom=-1
fcvt(x3, denom=0)  # as floating point or fractional number
fcvt(x3, denom=1)  # as fractional number except for integers
fcvt(x3, denom=8)  # as fractional number with denominator denom if possible

Description

firstmatch seeks matches for the elements of its first argument among those of its second. For further details please check base::charmatch(). charmatch returns a zero if multiple matches are found, whereas firstmatch returns the first partial match if multiple matches are found.

Usage

firstmatch(x, table, nomatch = NA_integer_)

Arguments

Value

An integer.

Examples

firstmatch("d", c("chisq", "cauchy"))
charmatch("c", c("chisq", "cauchy"))
firstmatch("c", c("chisq", "cauchy"))
firstmatch("ca", c("chisq", "cauchy"))

Description

Finds rational approximations to the components of a real numeric object, using a standard continued fraction method. Calls MASS::fractions() (Please refer to that for further details).

Usage

fractions(x, cycles = 10, max.denominator = 2000, ...)

approx_rational(x, cycles = 10, max.denominator = 2000, ...)

Arguments

Value

An object of the class fractions. A structure with a .Data component, the same as the numeric x input, but with the rational approximations held as the character vector attribute fracs. Arithmetic operations on fractions objects are possible.

Examples

X <- matrix(runif(25), 5, 5)
fractions(X) #;)
fractions(solve(X, X/5))
fractions(solve(X, X/5)) + 1

Description

Runs all combinations of elements in ... as parameters of FUN (grid apply). I(.) can be used to avoid that an element is interpreted as a grid value. If an error occurs, then the result of FUN will not be stored. You may notice missing indices in the returning list.

Usage

gapply(FUN, ..., .simplify = TRUE)

apply_grid(FUN, ..., .simplify = TRUE)

Arguments

Value

A list or a data frame with the function results.

Examples

# 8 function calls: sum(1,3,5), sum(1,3,6), ..., sum(2,4,6)
gapply("sum", 1:2, 3:4, 5:6)
# 4 function calls: sum(1,3,5:6), sum(1,4,5:66), ..., sum(2,4,5:6)
gapply("sum", 1:2, 3:4, I(5:6))

Description

Computes a grade based on the points of the grade scheme by the Humboldt University of Berlin. (See §96c and §102 in the Achte Änderung der Fächerübergreifenden Satzung zur Regelung von Zulassung, Studium und Prüfung der Humboldt-Universität zu Berlin (ZSP-HU))

Usage

grade(points, maxpts = max(points), fixed = TRUE)

hu_grade(points, maxpts = max(points), fixed = TRUE)

Arguments

Value

Grades as a function of points.

Examples

x <- round(runif(100, 0, 22.4))
grade(x, 22)

Description

Computes mean, mode or quantile/median of grouped data.

Usage

grouped_data(x, n, compute = c("mean", "fine", "coarse"), tol = 1e-06)

grouped_stats(x, n, compute = c("mean", "fine", "coarse"), tol = 1e-06)

dgrouped(x, n, compute = c("mean", "fine", "coarse"), tol = 1e-06)

Arguments

Value

A list with the class, result and a table.

Examples

x <- 1:4
n <- ddiscrete(runif(3))
grouped_data(x, n)

Description

Simplifies a hyperloop object if possible.

Usage

gsimplify(ga, exclude = NULL, subset = NULL)

simplify_hyperloop(ga, exclude = NULL, subset = NULL)

simple_hloop(ga, exclude = NULL, subset = NULL)

Arguments

Value

A data frame if possible, otherwise a list.

Examples

# calls: t.test(x, -1), t.test(x, 0), t.test(x, 1)
ga <- gapply(t.test, x=I(rnorm(100)), mu=-1:1)
# no simplication since `data.name` and `conf.int` have lengths larger  than one
gsimplify(ga)
#' simplification is now possible
gsimplify(ga, exclude=c("conf.int", "data.name"))

Description

Randomly selects size breakpoints from breaks. If outer is TRUE, then the first and last element of breaks is always included into the returned break points. If size is a vector, the number of breakpoints is first sampled from size.

Usage

histbreaks(breaks, size, outer = TRUE, ...)

rand_breaks(breaks, size, outer = TRUE, ...)

dhistbreaks(breaks, size, outer = TRUE, ...)

Arguments

Value

A vector of breakpoints.

Examples

# Always includes 100 and 200
histbreaks(seq(100, 200, by=10), 4)
# Always includes 100 and 200 and chooses randomly between 3 to 5 break points  
histbreaks(seq(100, 200, by=10), 3:5)           
# May not include 100 and 200
histbreaks(seq(100, 200, by=10), 4, outer=FALSE)

Description

Returns data for a histogram. Calls internally hist(..., plot=FALSE).

• mean returns the mean of the data.

• quantile and median return the quantile(s) or median with an attribute pos, the class number of the quantile(s), or the median.

Usage

histdata(x, breaks = "Sturges", probs = seq(0, 1, 0.25), ...)

## S3 method for class 'histogram'
quantile(x, probs = seq(0, 1, 0.25), ...)

## S3 method for class 'histogram'
median(x, ...)

## S3 method for class 'histogram'
mean(x, ...)

dhist(x, breaks = "Sturges", probs = seq(0, 1, 0.25), ...)

Arguments

Value

Like in graphics::hist, but with this additional list of elements:

• lower lower class borders,

• upper upper class borders,

• width class widths,

• relfreq the relative class frequency,

• cumfbrk the cumulated relative frequency of the breaks,

• maxdens the indices of the maximal density values,

• maxcount the indices of the maximal count values

• x the original finite data, and

• class the class number for each value in x.

Examples

#1
x <- seq(0, 1, by=0.25)
print(hist(x, plot=FALSE))
histdata(x)
#2
x <- seq(0, 1, by=0.25)
print(hist(x, x, plot=FALSE))
histdata(x, x)
#3
print(hist(x, x, right=FALSE, plot=FALSE))
histdata(x, x, right=FALSE)

Description

Creates a set of breaks and absolute frequencies in the range from 'from' to 'to'. The class widths are sampled from widths. The resulting numbers could be multiplied with an integer, if the sum(n) is too small. Additionally, it is checked whether the generated densities are terminating decimals.

Usage

histwidth(from, to, widths, dmax = 100)

width_breaks(from, to, widths, dmax = 100)

dhistwidth(from, to, widths, dmax = 100)

Arguments

Value

A list with breaks, n's for each class and decimal if all densities are terminating decimals.

Examples

l <- histwidth(1.6, 2.1, widths=c(0.05, 0.1, 0.15, 0.2))
l
x <- histx(l$breaks, l$n)
histdata(x, l$breaks)

Description

Given the breaks and the number of observations, a data set is generated with stats::runif(), using the class mids: $x_i = class\_mid_j + alpha*class\_width_j/2$. The default alpha=0.99 ensures that generated observations do not lie on the class borders.

Usage

histx(breaks, n, alpha = 0.99)

gen_mid(breaks, n, alpha = 0.99)

dhistx(breaks, n, alpha = 0.99)

Arguments

Value

The generated data set.

Examples

q  <- sort(sample(seq(0.1, 0.9, by=0.1), 4))
qx <- pnorm(q)
histx(qx, diff(q))

Description

• hm_cell or hm_index modify a data cell format (fmt="%s"), value (unnamed parameter) or style (text_align="left")

• hm_col or hm_row modify a row or column format (fmt="%s"), value (unnamed parameter) or style (text_align="left")

• hm_title modifies the title attribute of an html_matrix based on specific arguments

• hm_table modifies the properties of the entire HTML table within an html_matrix

• hm_tr modifies the properties of one or more table rows (tr elements) in an html_matrix. Row indices for modification (ind) can be specified along with additional parameters to customize the row format, values, or style

Usage

hm_cell(x, row = NULL, col = NULL, ..., byrow = FALSE)

hm_index(x, ind, ...)

hm_title(x, ...)

hm_table(x, ...)

hm_row(x, ind, ...)

hm_col(x, ind, ...)

hm_tr(x, ind, ...)

modify_cell(x, row = NULL, col = NULL, ..., byrow = FALSE)

mod_cell(x, row = NULL, col = NULL, ..., byrow = FALSE)

modify_col(x, ind, ...)

mod_col(x, ind, ...)

modify_index(x, ind, ...)

mod_ind(x, ind, ...)

modify_row(x, ind, ...)

mod_row(x, ind, ...)

modify_table(x, ...)

mod_t(x, ...)

modify_title(x, ...)

mod_title(x, ...)

modify_tr(x, ind, ...)

mod_tr(x, ind, ...)

Arguments

Value

A modified html_matrix object.

Examples

l <- html_matrix(matrix(1:6, ncol=2))
# replace l[1,1] by NA
hm_cell(l, 1, 1, NA)
# replace l[1,1] by NA and set the text_align to center
hm_cell(l, 1, 1, NA, text_align="center")
# replace l[1,3] and l[2,1] by NA
rcind <- cbind(c(1,3), c(2, 1))
hm_index(l, rcind, NA)
# set a new title
hm_title(l, "new title")
# set a new row or column title
hm_row(l, 2, "row 2")
hm_col(l, 1, "col 1")
# set fmt by column or row
print(hm_cell(l, fmt=c("%.0f", "%.1f", "%.2f"), byrow=FALSE), which="fmt")
print(hm_cell(l, fmt=c("%.0f", "%.1f"), byrow=TRUE), which="fmt")

Description

Creates an HTML page with all the contents of the XML tags whose names match pattern.

The default is to show the contents of all XML tags. The HTML page is stored in the HTML file name.

The default name=NULL creates a temporary file. If the name does not end in .html, then a .html is appended.

If browseURL=TRUE (default) then the HTML page will be displayed in the browser.

If necessary the contents of XML tags are concatenated with "\n". For single XML tags this can be changed, e.g. merge=list("questionlist"="<br>" leads to the XML tag <questionlist>...</questionlist>) "<br>" being used ,instead of the "\n".

Usage

html_e2m(
  exam,
  name = NULL,
  pattern = ".",
  mathjax = TRUE,
  browseURL = TRUE,
  overwrite = FALSE,
  header = 2,
  merge = list(questionlist = "<br>"),
  png = TRUE
)

toHTML_XML(
  exam,
  name = NULL,
  pattern = ".",
  mathjax = TRUE,
  browseURL = TRUE,
  overwrite = FALSE,
  header = 2,
  merge = list(questionlist = "<br>"),
  png = TRUE
)

Arguments

Value

Invisibly, the names of listed elements in the HTML file.

See Also

The aim is similar to exams:::exams:::browse_exercise, however, html_e2m takes the information form the XML file generated by the exams.forge package.

Examples

if (interactive()) {
  resexams <- readRDS(system.file("xml", "klausur-test.rds", package="exams.moodle"))
  html_e2m(resexams) # opens HTML file into browser
}

Description

Creates from a vector, a matrix, an array, or a table, an HTML representation of it. The HTML representation has one column and one row more than the data. The additional row and column are used in order to have a title (top left), the column names (top), and the row names (left).

You can set the style attributes (⁠<td style="...">⁠) via hm_cell, hm_title, hm_col, and hm_row. For example: hm_cell(hm, 1, 1, text_align="right") will lead to (⁠<td style="text-align:right;">⁠) for the cell (1,1), and any unnamed element will change the cell value. Note: since - is an operator in R, we use ⁠_⁠ instead. Of course, someone could use "text-align"="right", but I am lazy.

Usage

html_matrix(x, ...)

## Default S3 method:
html_matrix(
  x,
  ...,
  byrow = FALSE,
  numeric = list(text_align = "right"),
  integer = list(text_align = "right"),
  char = list(text_align = "left"),
  logical = list(text_align = "right"),
  border = "#999999"
)

html_mx(x, ...)

Arguments

Value

Returns an html_matrix.

Examples

m <- matrix(1:6, ncol=2)
m
l <- html_matrix(m)
l

Description

My personal pipe creating an html_matrix object. Note that the length of fmt must be either nrow(m) or ncol(m) depending on byrow.

   html_matrix(m) 
     tooltip(sprintf(tooltip, nrow(m), ncol(m))) 
     hm_cell(fmt=fmt, byrow=byrow)

Usage

html_matrix_sk(
  m,
  title,
  fmt,
  byrow = TRUE,
  tooltip = "Die Tabelle hat %.0f Zeilen und %.0f Spalten",
  ...
)

lmatrix(
  m,
  title,
  fmt,
  byrow = TRUE,
  tooltip = "Die Tabelle hat %.0f Zeilen und %.0f Spalten",
  ...
)

Arguments

Value

An html_matrix object.

Examples

m <- matrix(1:6, ncol=2)
html_matrix_sk(m, title="", fmt=c("%.0f", "%.1f"))

Description

Generates a data frame with potential values for m, n and k. If hyper2 is FALSE then the parametrization of stats::dhyper() is used, otherwise n+m, m and k is used and transformed to m, n and k. In accordance with specific conditions it holds that:

• if length(mean)==1 and it's an integer, it signifies the desired number of digits for the mean

• if mean is set to NA (the default), all means are permissible

• when length(mean) > 1, the product $k*m/(n+m)$ must be one of the valid means

• the same rules apply to sd

The parameters norm, pois and binom can take on the values NA, TRUE, FALSE, or be defined as a function of the format: ⁠function(m, n, k)⁠. These values determine which ⁠(m, n, k)⁠ combinations are eligible:

• for NA, all combinations of ⁠(m, n, k)⁠ are acceptable

• if specified as a function, only those combinations for which the function evaluates to TRUE are considered valid

• if set to TRUE, combinations are accepted only if they satisfy either the condition $k*m/(m+n)*(1-m/(m+n))>=9$ (for norm, indicating a normal distribution approximation), the conditions $k/(n+m) < 0.05$, $m/(n+m) < 0.05$ and $k>10$ (for pois, implying a Poisson distribution approximation) and the condition $k/(n+m) < 0.05$ (for binom, implying a binomial distribution approximation)

• if set to FALSE, the approximations should not hold for any combination.

Please be aware that there is no guarantee that the resulting data frame will include a valid solution.

Usage

hyper_param(
  m,
  n,
  k,
  mean = NA,
  sd = NA,
  norm = NA,
  pois = NA,
  binom = NA,
  tol = 1e-06,
  hyper2 = FALSE
)

Arguments

Value

A data frame with possible the choices of n , p, mean and sd.

Examples

hyper_param(7:14, 1:13, 3:10, norm=FALSE, pois=FALSE, binom=FALSE, hyper2=TRUE)

Description

Runs a function several times with all parameter combinations, and checks:

• if an argument is not a list, then it will be converted to an one element list

• if an error occurs then the result of FUN will not be stored

Usage

hyperloop(FUN, ..., .simplify = FALSE)

hloop(FUN, ..., .simplify = FALSE)

Arguments

Value

A hyperloop object as a list.

Examples

x   <- rnorm(100)
trm <- hyperloop(mean, x=list(x), trim=as.list(seq(0, 0.5, by=0.05)))
# automatic conversion of x to list(x)
trm <- hyperloop(mean, x=x, trim=as.list(seq(0, 0.5, by=0.05))) 
unlist(trm)

Description

Creates a data frame for a test hypothesis with various columns:

• h0.left left value of the null hypothesis, usually ⁠\mu⁠ or ⁠\pi⁠

• h0.operator operator of the null hypothesis, one of the following: eq, ne, lt, le, gt, or ge

• h0.right right value of the null hypothesis, usually ⁠\mu_0⁠, ⁠\pi_0⁠, or a hypothetical value

• h1.left left value of the alternative hypothesis, usually ⁠\mu⁠ or ⁠\pi⁠

• h1.operator operator of the alternative hypothesis, one of the following: eq, ne, lt, le, gt, or ge

• h1.right right value of the alternative hypothesis, usually ⁠\mu_0⁠, ⁠\pi_0⁠, or a hypothetical value

• H0 latex representation of the null hypothesis

• H1 latex representation of the alternative hypothesis

• match.left do the left value in the null and the alternative hypothesis match?

• match.right do the right value in the null and the alternative hypothesis match?

• match.operator do the operators in the null and the alternative hypothesis cover all real numbers?

• match.right do the right value in the null and alternative hypothesis match?

• match.type either wrong, left.sided, right.sided, two.sided, greater, or less.

If null is not given then it is determined from alternative. Otherwise hypotheses pairs are generated by all combinations from alternative and null. Valid values for alternativeand null are two.sided, greater, less, eq, ne, lt, le, gt, or ge.

Usage

hypothesis_latex(
  left,
  alternative = NULL,
  null = NULL,
  right = paste0(left, "_0")
)

lhypo(left, alternative = NULL, null = NULL, right = paste0(left, "_0"))

Arguments

Value

A data frame with hypothesis pairs.

Examples

# Create one hypotheses pair
hypothesis_latex("\\mu")
hypothesis_latex("\\pi")
hypothesis_latex("\\mu", alternative="two.sided")
hypothesis_latex("\\mu", alternative="two.sided", null="lt")
hypothesis_latex("\\mu", alternative="ne", null="eq")
hypothesis_latex("\\mu", right=c(0,1))
hypothesis_latex("\\mu", alternative=c("eq", "ne", "lt", "le", "gt", "ge"))
hypothesis_latex("\\mu", alternative=c("eq", "ne", "lt", "le", "gt", "ge"), 
                         null=c("eq", "ne", "lt", "le", "gt", "ge"))

Description

Fills a relative contingency table with n missing values, such that the table entries can be recomputed. In case that no solution can be found, an error is generated.

Usage

incomplete_table(tab, n, maxit = 1000)

cont_table_fill(tab, n, maxit = 1000)

Arguments

Value

A contingency table including marginal values and total sum with missing values. The attribute fillin gives the necessary information about the order in which the entries can be calculated, while the attribute full presents the contingency table, including marginal values and total sum.

Examples

tab <- rbind(c(0.02, 0.04, 0.34), c(0.02, 0.28, 0.3))
incomplete_table(tab, 7)

Description

Knits txt within an R code chunk.

Usage

inline(txt)

txt_knit(txt)

Arguments

Value

Output.

Examples

result <- inline("2 + 2")

Description

Checks if x is in an opened or closed interval between min and max. The default is set as such, that the chosen interval is an interval of $(0,1)$. For example, in the case of x being a probability.

Usage

is.prob(x, open = TRUE, min = 0, max = 1)

is_prob_interval(x, open = TRUE, min = 0, max = 1)

is_prob(x, open = TRUE, min = 0, max = 1)

in_range(x, open = TRUE, min = 0, max = 1)

Arguments

Value

A logical vector with the same length as x.

Examples

is.prob(runif(1))

Description

Selects a text argument and returns the knitted result.

Usage

knitif(n, ..., envir = knit_global())

knit_select(n, ..., envir = knit_global())

Arguments

Value

A character.

Examples

knitif(runif(1)<0.5, 'TRUE'="`r pi`", 'FALSE'="$\\pi=`r pi`$")

Description

If exams is called by exams2pdf,

• latexdef adds a TeX macro by ⁠\def\name{body}⁠ and

• answercol adds a ⁠\def\answercol{n}⁠ to modify the number of output columns for multiple-choice answers to the LaTeX file.

Usage

latexdef(name, body)

answercol(n)

add_answercol_def(n)

Arguments

Value

Nothing

Examples

answercol(2)

Description

Computes the least common multiple for a numeric vector x.

Usage

lcmval(x)

lcm_vector(x)

Arguments

Value

The least common multiple.

Examples

lcmval(c(144, 160))      # = 1440
lcmval(c(144, 160, 175)) # = 50.400

Description

Creates data suitable for a simple linear regression. In the first step, data is computed using pearson_data(), satisfying the conditions $\sum_{i=1}^{nmax} x_i^2 = n$ and $\sum_{i=1}^{nmax} x_i = 0$ (similar conditions apply to $y$. The data are then rescaled with $x' = center[1]+scale[1]*x$ and $y' = center[2]+scale[2]*y$. Finally, a simple linear regression is performed on the transformed data.