Distribution: Class distribution

In sigbertklinke/exams2moodle: Access routines to XML Moodle files and helper routines to simplify generating exercises for Moodle from the 'exams' package

Class distribution

Description

Holds a univariate distribution including its parameters. The name of the distribution is used to determine, for example the 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 cumulative distribution function must exist.

The following functions exists for disributions:

• distribution creates a distribution with name 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 if 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, ...)

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)

Arguments

name	character: a replacement of the name of the distribtuion type
...	further named distribution parameters
discrete	logical: Is distribution discrete? (default: NA)
x	vector of values
probs	numeric: vector of probabilities with values in [0,1].
q	numeric: vector of quantiles
d	distribution
object	distribution object
param	character: names for the distribution parameters
digits	integer: number of digits used in signif
min	numeric: left border of interval
max	numeric: right border of interval
tol	numeric: tolerance for max==min (default: 1e-6)

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)
# see the LaTeX names
data(distributions)
distributions

sigbertklinke/exams2moodle documentation built on July 6, 2023, 3:26 p.m.