# Davies: The Davies distribution In Davies: The Davies Quantile Function

## Description

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

## Usage

 ```1 2 3 4 5``` ``` 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 , lambda1 and~lambda2

## 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.

## 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

`Gld`, `fit.davies.p`, `least.squares`, `skewness`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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") ```