LNORM3: Three-Parameter Lognormal Distribution

In FAdist: Distributions that are Sometimes Used in Hydrology

Three-Parameter Lognormal Distribution

Description

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

Usage

dlnorm3(x,shape=1,scale=1,thres=0,log=FALSE)
plnorm3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
qlnorm3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
rlnorm3(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 normal distribution (with location(mean) and scale(standard deviation) parameters), then X = exp(Y)+m has a 3-parameter lognormal distribution with shape and scale parameters corresponding to the scale and location parameteres of Y, respectively; and threshold parameter m.

Value

dlnorm3 gives the density, plnorm3 gives the distribution function, qlnorm3 gives the quantile function, and rlnorm3 generates random deviates.

See Also

dnorm, pnorm, qnorm, rnorm, dlnorm, plnorm, qlnorm, rlnorm

Examples

m <- 100
x <- rlnorm3(10,1,0,m)
dlnorm3(x,1,0,m)
dlnorm(x-m,0,1)
dnorm(log(x-m),0,1)/(x-m)

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