GAMMA3: Three-Parameter Gamma Distribution (also known as Pearson...

In FAdist: Distributions that are Sometimes Used in Hydrology

Three-Parameter Gamma Distribution (also known as Pearson type III distribution)

Description

Density, distribution function, quantile function and random generation for the 3-parameter gamma distribution with shape, scale, and threshold (or shift) parameters equal to shape, scale, and thres, respectively.

Usage

dgamma3(x,shape=1,scale=1,thres=0,log=FALSE)
pgamma3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
qgamma3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
rgamma3(n,shape=1,scale=1,thres=0)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations.
shape	shape parameter.
scale	scale parameter.
thres	threshold or shift parameter.
log,log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Details

If Y is a random variable distributed according to a gamma distribution (with shape and scale parameters), then X = Y+m has a 3-parameter gamma distribution with the same shape and scale parameters, and with threshold (or shift) parameter m.

Value

dgamma3 gives the density, pgamma3 gives the distribution function, qgamma3 gives the quantile function, and rgamma3 generates random deviates.

References

Bobee, B. and F. Ashkar (1991). The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publications, Littleton, Colo., 217 p.

See Also

dgamma, pgamma, qgamma, rgamma

Examples

thres <- 10
x <- rgamma3(n=10,shape=2,scale=11,thres=thres)
dgamma3(x,2,11,thres)
dgamma(x-thres,2,1/11)

FAdist documentation built on March 18, 2022, 5:24 p.m.