JSB {skewunit} | R Documentation |
The Johnson S_B
distribution.
Description
Density, distribution function and random generation for the Johnson S_B
distribution.
Usage
dJSB(x, delta=1, log=FALSE)
pJSB(q, delta=1, lower.tail=TRUE, log.p=FALSE)
rJSB(n, delta=1)
Arguments
x , q |
vector of quantiles. |
n |
number of observations. If length(n) > 1, the length is taken to be the number required. |
delta |
shape parameter (by default is 1). |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
Details
The Johnson S_B
distribution has density
f(x)=\frac{\delta}{x(1-x)}\phi\left(\delta \eta(x)\right), \quad x \in (0,1),
where \eta(x)=\log(\frac{x}{1-x})
, \phi(\cdot)
denotes the density of the
standard normal distribution and \delta>0
. Its cumulative distribution function is
F(x)=\Phi\left(\delta \eta(x)\right), \quad x \in (0,1),
where \Phi(\cdot)
is the cumulative distribution function of the
standard normal distribution.
Value
dJSB gives the density, pJSB gives the distribution function, and rJSB 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
References
Kotz, S., van Dorp, J.R. (2004). Beyond Beta. Other Continuous Families of Distributions with Bounded Support and Applications. World Scientific.
Examples
dJSB(0.5, 1.2)
pJSB(0.5, 0.5)
rJSB(5, 1.5)