PowerExponential {rmutil} R Documentation

## Power Exponential Distribution

### Description

These functions provide information about the power exponential distribution with mean parameter equal to `m`, dispersion equal to `s`, and family parameter equal to `f`: density, cumulative distribution, quantiles, log hazard, and random generation.

The power exponential distribution has density

f(y) = exp(-(abs(y-m)/sqrt(s))^(2 f)/2)/ (sqrt(s) Gamma(1+1/(2 f)) 2^(1+1/(2 f)))

where m is the mean of the distribution, s is the dispersion, and f is the family parameter. f=1 yields a normal distribution, f=0.5 a Laplace distribution, and f=Inf a uniform distribution.

### Usage

```dpowexp(y, m=0, s=1, f=1, log=FALSE)
ppowexp(q, m=0, s=1, f=1)
qpowexp(p, m=0, s=1, f=1)
rpowexp(n, m=0, s=1, f=1)
```

### Arguments

 `y` vector of responses. `q` vector of quantiles. `p` vector of probabilities `n` number of values to generate `m` vector of means. `s` vector of dispersion parameters. `f` vector of family parameters. `log` if TRUE, log probabilities are supplied.

J.K. Lindsey

### Examples

```dpowexp(5, 5, 1, 2)
ppowexp(5, 5, 1, 2)
qpowexp(0.5, 5, 1, 2)
rpowexp(10, 5, 1, 2)
```

[Package rmutil version 1.0 Index]