Pearson {PearsonDS}

The Pearson Distribution System

Description

Density, distribution function, quantile function and random generation for the Pearson distribution system.

Usage

dpearson(x, params, moments, log = FALSE, ...)

ppearson(q, params, moments, lower.tail = TRUE, log.p = FALSE, ...)

qpearson(p, params, moments, lower.tail = TRUE, log.p = FALSE, ...)

rpearson(n, params, moments, ...)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

params

vector/list of parameters for Pearson distribution. First entry gives type of distribution (0 for type 0, 1 for type I, ..., 7 for type VII), remaining entries give distribution parameters (depending on distribution type).

moments

optional vector/list of mean, variance, skewness, kurtosis (not excess kurtosis). Overrides params with corresponding pearson distribution, if given.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE, probabilities are P[X\le x], otherwise, P[X>x].

...

further parameters for underlying functions (currently only used for distributions of type IV).

Details

These are the wrapper functions for the (d,p,q,r)-functions of the Pearson distribution system sub-classes.

Value

dpearson gives the density, ppearson gives the distribution function, qpearson gives the quantile function, and rpearson generates random deviates.

Author(s)

Martin Becker [e-mail]

See Also

PearsonDS-package, Pearson0, PearsonI, PearsonII, PearsonIII, PearsonIV, PearsonV, PearsonVI, PearsonVII, pearsonFitM, pearsonFitML, pearsonMSC

Examples

## Define moments of distribution
moments <- c(mean=1,variance=2,skewness=1,kurtosis=5)
## Generate some random variates
rpearson(5,moments=moments)
## evaluate distribution function
ppearson(seq(-2,3,by=1),moments=moments)
## evaluate density function
dpearson(seq(-2,3,by=1),moments=moments)
## evaluate quantile function
qpearson(seq(0.1,0.9,by=0.2),moments=moments)