# pnormp: Probability function of an exponential power distribution In normalp: Routines for Exponential Power Distribution

## Description

Probability function for the exponential power distribution with location parameter `mu`, scale parameter `sigmap` and shape parameter `p`.

## Usage

 `1` ```pnormp(q, mu=0, sigmap=1, p=2, lower.tail=TRUE, log.pr=FALSE) ```

## Arguments

 `q` Vector of quantiles. `mu` Vector of location parameters. `sigmap` Vector of scale parameters. `p` Shape parameter. `lower.tail` Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X>x]. `log.pr` Logical; if TRUE, probabilities pr are given as log(pr).

## Details

If `mu`, `sigmap` or `p` are not specified they assume the default values 0, 1 and 2, respectively. The exponential power distribution has density function

f(x) = 1/(2 p^(1/p) Gamma(1+1/p) sigmap) exp{-|x - mu|^p/(p sigmap^p)}

where mu is the location parameter, sigmap the scale parameter and p the shape parameter. When p=2 the exponential power distribution becomes the Normal Distribution, when p=1 the exponential power distribution becomes the Laplace Distribution, when p->infinity the exponential power distribution becomes the Uniform Distribution.

## Value

`pnormp` gives the probability of an exponential power distribution.

## Author(s)

Angelo M. Mineo

`Normal` for the Normal distribution, `Uniform` for the Uniform distribution, and `Special` for the Gamma function.

## Examples

 ```1 2 3 4 5 6 7``` ```## Compute the distribution function for a vector x with mu=0, sigmap=1 and p=1.5 ## At the end we have the graph of the exponential power distribution function with p=1.5. x <- c(-1, 1) pr <- pnormp(x, p=1.5) print(pr) plot(function(x) pnormp(x, p=1.5), -4, 4, main = "Exponential Power Distribution Function (p=1.5)", ylab="F(x)") ```

### Example output ``` 0.1699012 0.8300988
```

normalp documentation built on Feb. 14, 2020, 5:08 p.m.