rpn function

The PN distribution

Density, distribution function, quantile function and random generation for the PN distribution with power equal to alpha.

dpn(x, alpha)
ppn(q, alpha)
qpn(p, alpha)
rpn(n, alpha)

Arguments

• x, q: vector of observations or quantiles.
• p: vector of probabilities.
• n: number of observations.
• alpha: power parameter.

Details

The alpha parameter must be greater than 0 (alpha > 0).

References

Lehmann, EL. (1953). The power of rank tests. The Annals of Mathematical Statistics, 24 , 23--43.

Durrans, SR. (1992). Distributions of fractional order statistics in hydrology. Water Resources Research, 28 , 1649--1655.

Agamez-Montavo, G. (2017). Modelos de mistura finita usando a classe de distribuicoes alpha potencia. Thesis (Doctoral), University of Sao Paulo.

Examples

# Density

dpn(2,1)
dnorm(2)

# Distribution function

ppn(2,1)
pnorm(2)

# Quantile function

qpn(0.5,1)
qnorm(0.5)

# Random generation

alpha <- 0.5
n <- 10
rpn(n, alpha)