Davies (version 1.1-5)

Davies: The Davies distribution

Description

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

Usage

ddavies(x, params)
 pdavies(x, params)
 qdavies(p, params)
 rdavies(n, params)
ddavies.p(x,params)

Arguments

x

quantile

p

vector of probabilities

n

number of observations. If length(n) > 1, the length is taken to be the number required

params

A three-member vector holding~$C$ , $\lambda_1$ and~$\lambda_2$

Value

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

Details

The Davies distribution is defined in terms of its quantile function: $$Cp^{\lambda_1}(1-p)^\lambda_2$$

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

References

draft MS available from the author on request

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")