R Programming/Probability Functions

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Contents 1 Overview 2 Normal and related distributions 3 Extreme values and related distribution 4 Discrete distributions 5 Distribution for circular statistics 6 Getting the quantile

[edit] Overview

R has lots of probability functions.

• r is the generic prefix for random variable generator such as runif(), rnorm()
• d is the generic prefix for the probability density function (therefore pdf).
• p is the generic prefix for the cumulative density function (therefore cdf)
• q is the generic prefix for the quantile function (or inverse cdf).

Distribution	Keyword	Package	CDF	Quantile	PDF	Random Deviates
Student	TDist	stats	pt	qt	dt	rt
Beta	Beta	stats	pbeta	qbeta	dbeta	rbeta
Cauchy	Cauchy	stats	pcauchy	qcauchy	dcauchy	rcauchy
Gamma	GammaDist	stats
Logistic		stats	plogis	qlogis	dlogis	rlogis
Weibull		stats
Dirichlet		gtools
Dirichlet		MCMCpack
InvGamma		MCMCpack
InvWishart		MCMCpack
Burr	Burr	actuar	dburr	pburr	qburr	rburr
Pareto		actuar	dpareto	ppareto	rpareto	qpareto
Gumbel		evd	dgumbel
Frechet		evd	dfrechet
Generalized Pareto		evd	dgpd
Generalized Extreme Value		evd	dgev

• • Geometric
  • Hypergeometric
  • Tukey
  • Wilcoxon
• See also the "SuppDists" package.

[edit] Normal and related distributions

• The mvtnorm package includes functions for multivariate normal distributions.
  • TDist
  • Chisquare
  • FDist
  • Lognormal
  • Normal

[edit] Extreme values and related distribution

• The Gumbel Distribution
• The logistic distribution : distribution of the difference of two gumbel distributions.

[edit] Discrete distributions

• • Binomial
• Poisson
  • Multinomial
  • NegBinomial

[edit] Distribution for circular statistics

• Functions for circular statistics are included in the CircStats package.
  • dvm() Von Mises density function
  • dtri() triangular density function
  • dmixedvm() Mixed Von Mises density
  • dwrpcauchy() wrapped cauchy density
  • dwrpnorm() wrapped normal density.

[edit] Getting the quantile

Some quantile are very useful, especially when you have to construct confidence interval or to test an hypothesis.

Quantile of the normal distribution

> qnorm(.95)
[1] 1.644854
> qnorm(.975)
[1] 1.959964
> qnorm(.99)
[1] 2.326348

Quantile of the Student t distribution

> qt(.975,30)
[1] 2.042272
> qt(.975,100)
[1] 1.983972
> qt(.975,1000)
[1] 1.962339

Quantile of the χ² distribution

> qchisq(.95,1)
[1] 3.841459
> qchisq(.95,10)
[1] 18.30704
> qchisq(.95,100)
[1] 124.3421

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Index

Next: Random Number Generation