rmutil (version 1.1.4)

PowerExponential: 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 $$ f(y) = \frac{\exp(-(abs{y-\mu}/\sqrt{\sigma})^{2 \nu}/2)}{ \sqrt{\sigma} Gamma(1+1/(2 \nu)) 2^{1+1/(2 \nu)}}$$

where \(\mu\) is the mean of the distribution, \(\sigma\) is the dispersion, and \(\nu\) is the family parameter. \(\nu=1\) yields a normal distribution, \(\nu=0.5\) a Laplace distribution, and \(\nu=\infty\) 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.

Examples

# NOT RUN {
dpowexp(5, 5, 1, 2)
ppowexp(5, 5, 1, 2)
qpowexp(0.5, 5, 1, 2)
rpowexp(10, 5, 1, 2)
# }