FAdist (version 2.0)

LGAMMA3: Log-Pearson Type III Distribution

Description

Density, distribution function, quantile function and random generation for the log-Pearson type III distribution with shape1, shape2, and scale parameters equal to shape, scale, and thres, respectively.

Usage

dlgamma3(x,shape=1,scale=1,thres=1,log=FALSE)
plgamma3(q,shape=1,scale=1,thres=1,lower.tail=TRUE,log.p=FALSE)
qlgamma3(p,shape=1,scale=1,thres=1,lower.tail=TRUE,log.p=FALSE)
rlgamma3(n,shape=1,scale=1,thres=1)

Arguments

x,q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

shape

shape1 parameter.

scale

shape2 parameter.

thres

scale 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]<="" em="">,otherwise, P[X > x].

Value

• dlgamma3 gives the density, plgamma3 gives the distribution function, qlgamma3 gives the quantile function, and rlgamma3 generates random deviates.

Details

If Y is a random variable distributed according to a gamma distribution (with shape and scale parameters), then X = exp(Y+m) has a log-Pearson type III distribution with shape1 and shape2 parameters corresponding to the shape and 1/scale parameteres of Y, and with scale parameter m.

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, dgamma3, pgamma3, qgamma3, rgamma3

Examples

thres <- 10
x <- rlgamma3(n=10,shape=2,scale=11,thres=thres)
dlgamma3(x,2,11,thres)
dgamma3(log(x),2,1/11,thres)/x
dgamma(log(x)-thres,2,11)/x