Distribution: Class Distribution

In exams.forge: Support for Compiling Examination Tasks using the 'exams' Package

Class Distribution

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

name	character: a replacement of the name of the distribution type
...	further named distribution parameters
discrete	logical: is the distribution discrete? (default: NA)
x	vector of values
probs	numeric: vector of probabilities with values in [0,1].
q	numeric: vector of quantiles
object	distribution object
d	distribution
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)

exams.forge documentation built on Sept. 11, 2024, 5:32 p.m.