dnormp {normalp}R Documentation

Density function of a Normal of Order p Distribution

Description

Density function for the normal of order p distribution with location parameter mu, scale parameter sigmap and structure parameter p.

Usage

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

Arguments

x Vector of quantiles.
mu Vector of location parameters.
sigmap Vector of scale parameters.
p Structure parameter.
log Logical; if TRUE, the density is given as log(density).

Details

If mu, sigmap or p are not specified they assume the default values 0, 1 and 2, respectively. The normal of order p 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 structure parameter. When p=2 the Normal of Order p Distribution becomes the Normal (Gaussian) Distribution, when p=1 the Normal of Order p Distribution becomes the Laplace Distribution, when p->infinity the Normal of Order p Distribution becomes the Uniform Distribution.

Value

dnormp gives the density function of a normal of order p distribution.

Author(s)

Angelo M. Mineo

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 Normal of order p 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 = "Normal of order p Density function (p=1.5)", ylab="f(x)")

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