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. ( |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
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)