rpn: The PN distribution

In PowerNormal: Power Normal Distribution

Description

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

Usage

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)

Example output

[1] 0.05399097
[1] 0.05399097
[1] 0.9772499
[1] 0.9772499
[1] 0
[1] 0
 [1] -1.11349800  0.67047194 -0.09584167 -1.19020494 -3.17941827 -1.12831851
 [7] -4.91638739  0.04278035 -0.69266186 -1.57085479

PowerNormal documentation built on May 2, 2019, 7:31 a.m.