Davies: The Davies distribution

In Davies: The Davies Quantile Function

The Davies distribution

Description

\loadmathjax

Density, distribution function, quantile function and random generation for the Davies distribution.

Usage

 ddavies(x, params,log=FALSE)
 pdavies(x, params,log.p=FALSE,lower.tail=TRUE)
 qdavies(p, params,lower.tail=TRUE)
 rdavies(n, params)
ddavies.p(x,params,log=FALSE)

Arguments

x	quantile
p	vector of probabilities
n	number of observations. If length(n) > 1, the length is taken to be the number required
lower.tail	logical; if TRUE (default), probabilities are \mjeqnP(X\leq x)P[X <= x], otherwise \mjeqnP(X>x)P[X > x]
log,log.p	logical; if TRUE, probabilities are given as \mjseqn\log(p)
params	A three-member vector holding \mjeqnCC, \mjeqn\lambda_1lambda1 and \mjeqn\lambda_2lambda2

Details

The Davies distribution is defined in terms of its quantile function:

Cp^lambda_1/(1-p)^lambda2

It does not have a closed-form probability density function or cumulative density function, so numerical solution is used.

Function ddavies.p() returns the density of the Davies function but as a function of the quantile.

Value

Function ddavies() gives the density, pdavies() gives the distribution function, qdavies() gives the quantile function, and rdavies() generates random deviates.

Author(s)

Robin K. S. Hankin

References

R. K. S. Hankin and A. Lee 2006. “A new family of non-negative distributions” Australia and New Zealand Journal of Statistics, 48(1):67–78

See Also

Gld, fit.davies.p, least.squares, skewness

Examples

params <- c(10,0.1,0.1)
x <- seq(from=4,to=20,by=0.2)
p <- seq(from=1e-3,to=1-1e-3,len=50)

rdavies(n=5,params)
least.squares(rdavies(100,params))
plot(pdavies(x,params))


plot(p,qdavies(p,params))
plot(x,ddavies(x,params),type="b")

Davies documentation built on March 18, 2022, 5:52 p.m.