pjsb: Computing the cumulative distribution function of Johnson's...

In ForestFit: Statistical Modelling for Plant Size Distributions

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\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 \xi<x<\lambda+\xi, \Theta=(\delta,\gamma,\lambda,\xi)^T with \delta, \lambda> 0, -\infty<\gamma<\infty, and -\infty<\xi<\infty.

Usage

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

Arguments

data	Vector of observations.
param	Vector of the parameters \delta, \gamma, \lambda, and \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)

ForestFit documentation built on April 3, 2025, 5:27 p.m.