Uquad {skewunit}R Documentation

The U-quadratic distribution

Description

Density, distribution function and random generation for the U-quadratic distribution.

Usage

dUquad(x, a=0, b=1, log=FALSE)
pUquad(q, a=0, b=1, lower.tail=TRUE, log.p=FALSE)
rUquad(n, a=0, b=1)

Arguments

x, q

vector of quantiles.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

a, b

range of variable x. (a<b).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X\leq x], otherwise, P[X>x].

Details

The U-quadratic distribution has density

f(x) = \alpha (x-\beta)^2, \quad x\in (a,b), a\leq x \leq b,

where \alpha=12/(b-a)^3 and \beta=(a+b)/2. Its cumulative distribution function is

F(x) = \frac{\alpha}{3}[(x-\beta)^3+(\beta-a)^3], \quad x\in (a,b).

Value

dUquad gives the density, pUquad gives the distribution function, and rUquad generates random deviates. The length of the result is determined by n for rasin, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Author(s)

Diego Gallardo

Examples

dUquad(0.5)
pUquad(0.5)
rUquad(5)

[Package skewunit version 1.0 Index]