JSB: 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)

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.

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 $P[X\leq x]$, otherwise, $P[X>x]$.

Author

Diego Gallardo

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.

References

Kotz, S., van Dorp, J.R. (2004). Beyond Beta. Other Continuous Families of Distributions with Bounded Support and Applications. World Scientific.

Examples

Run this code

dJSB(0.5, 1.2)
pJSB(0.5, 0.5)
rJSB(5, 1.5)

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