Probability distributions

It is possible to find the the density, probability at the left of a point, quantile and random numbers for several distributions. For example, for a normal distribution:

• dnorm(x) for the density at x

• pnorm(x) for the probability to the left of x (cdf at x)

• qnorm(p) for the quantile, the probability to the left of qnorm(p) is p

• rnorm(n) generates a random sample of size n.

For example:

> a_seq(-5,5,by=.2)
> a
 [1] -5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2
[16] -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2  0.0  0.2  0.4  0.6  0.8
[31]  1.0  1.2  1.4  1.6  1.8  2.0  2.2  2.4  2.6  2.8  3.0  3.2  3.4  3.6  3.8
[46]  4.0  4.2  4.4  4.6  4.8  5.0
> a2_(pnorm(a))
> b_cbind(a,a2)

generates is table of the normal distribution. You can add parameter of the mean and standard deviation pnorm(a, nu,sigma)=pnorm((a-nu)/sigma)

> pnorm(1,0,3)
[1] 0.6305586
> pnorm(1,mean=0,sd=3)
[1] 0.6305587 
> pnorm(1/3)
[1] 0.6305586

You can name the parameters:

> pnorm(1,sd=2,mean=0)
[1] 0.6914625
> pnorm(mean=0,sd=2,1)
[1] 0.6914625
> pnorm(1,0,2)
[1] 0.6914625

The following is a list of distributions and their associated commands:

Beta  

dbeta, pbeta, qbeta, rbeta

pamameters: shape1, shape2

defaults: -, -

Binomial

dbinom, pbinom, qbinom, rbinom

pamameters: size, prob

defaults: -, -

Cauchy

dcauchy, pcauchy, qcauchy, rcauchy

pamameters: loc, scale

defaults: 0, 1

Chi-Square

dchisq, pchisq, qchisq, rchisq

pamameters: df

defaults: -

Exponential

dexp, pexp, qexp, rexp

pamameters: rate (the rate is the inverse of the mean of the distribution)

defaults: -

Double exponential

ddexp, pdexp, qdexp, rdexp

pamameters: -

defaults: -

Geometric

dgeom, pgeom, qgeom, rgeom

pamameters: prob

defaults: -

Hypergeometric

dhyper, phyper, qhyper, rhyper

pamameters:

defaults:

Lognormal

dlnorm, plnorm, qlnorm, rlnorm

pamameters:

defaults:

Logistic

dlogis, plogis, qlogis, rlogis

pamameters: loc, scale

defaults: 0, 1

Multivariate normal

dmvnorm, pmvnorm, qmvnorm, rmvnorm

pamameters: mean, cov, sd, rho, d

defaults:

Negative binomial

dnbinom, pnbinom, qnbinom, rnbinom

pamameters:

defaults:

Normal

dnorm, pnormqnorm, rnorm

pamameters:mean, sd

defaults: 0, 1

Poisson

dpois, ppois, qpois, rpois

pamameters: lambda

defaults: -

Student's t statistic

dt, pt, qt, rt

pamameters: df

defaults: -

Uniform

dunif, punif, qunif, runif

pamameters: min, max

defaults: 0, 1

Weibull

dweibull, pweibul, qweibul, rweibul

pamameters: shape

defaults: -

Wilcoxon Rank Sum Statistic

dwilcox, pwilcox, qwilcox, rwilcox

pamameters: m, n

defaults:

Comments to: Miguel A. Arcones

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