pjsb {ForestFit}R Documentation

Computing the cumulative distribution function of Johnson's SB (JSB) distribution

Description

Computes the cumulative distribution function of the four-parameter JSB distibution given by

F(xΘ)=ξxδλ2π(uξ)(λ+ξu)exp{12[γ+δlog(uξλ+ξu)]2}du, F\bigl(x\big|\Theta\bigr) = \int_{\xi}^{x}\frac {\delta \lambda}{\sqrt{2\pi}(u-\xi)(\lambda+\xi-u)}\exp\Biggl\{-\frac{1}{2}\Bigg[\gamma+\delta\log \biggl(\frac{u-\xi}{\lambda+\xi-u}\biggr) \Bigg]^2\Biggr\} du,

where ξ<x<λ+ξ\xi<x<\lambda+\xi, Θ=(δ,γ,λ,ξ)T\Theta=(\delta,\gamma,\lambda,\xi)^T with δ,λ>0\delta, \lambda> 0, <γ<-\infty<\gamma<\infty, and <ξ<-\infty<\xi<\infty.

Usage

pjsb(data, param, log.p = FALSE, lower.tail = TRUE)

Arguments

data

Vector of observations.

param

Vector of the parameters δ\delta, γ\gamma, λ\lambda, and ξ\xi.

log.p

If TRUE, then log(cdf) is returned.

lower.tail

If FALSE, then 1-cdf is returned.

Value

A vector of length n, giving random generated values from JSB distribution.

Author(s)

Mahdi Teimouri

Examples

data<-rnorm(10)
param<-c(delta<-1, gamma<-3, lambda<-12, xi<-5)
pjsb(data, param, log.p = FALSE, lower.tail = TRUE)

[Package ForestFit version 2.2.3 Index]