normalp (version 0.7.2)

dnormp: Density function of an exponential power distribution

Description

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

Usage

dnormp(x, mu=0, sigmap=1, p=2, log=FALSE)

Value

dnormp gives the density function of an exponential power distribution.

Arguments

x

Vector of quantiles.

mu

Vector of location parameters.

sigmap

Vector of scale parameters.

p

Shape parameter.

log

Logical; if TRUE, the density is given as log(density).

Author

Angelo M. Mineo

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

$$f(x) = \frac{1}{2 p^{(1/p)} \Gamma(1+1/p) \sigma_p} e^{-\frac{|x - \mu|^p}{p \sigma_p^p}}$$

where \(\mu\) is the location parameter, \(\sigma_p\) 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 \(p\rightarrow\infty\) the exponential power distribution becomes the Uniform Distribution.

See Also

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

Examples

## Compute the density 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 
## density function with p=1.5
x <- c(-1, 1)
f <- dnormp(x, p=1.5)
print(f)
plot(function(x) dnormp(x, p=1.5) , -4, 4,
          main = "Exponential power distribution density function (p=1.5)", ylab="f(x)")