qnormp {normalp}R Documentation

Quantiles of a Normal of Order p Distribution

Description

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

Usage

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

Arguments

pr Vector of probabilities.
mu Vector of location parameters.
sigmap Vector of scale parameters.
p Structure 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 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

qnormp gives the quantiles of a normal of order p distribution.

Author(s)

Angelo Mineo

See Also

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

Examples

## Compute the quantiles for a vector of probabilities x
## with mu=1, sigmap=2 and p=1.5
x <- 0.3
q <- qnormp(x, 1, 2, 1.5)
q

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