pjsb

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 $\xi&lt;x&lt;\lambda+\xi$, $\Theta=(\delta,\gamma,\lambda,\xi)^T$ with $\delta, \lambda&gt; 0$, $-\infty&lt;\gamma&lt;\infty$, and $-\infty&lt;\xi&lt;\infty$.

Developed for the following tasks. 1 ) Computing the probability density function,
cumulative distribution function, random generation, and estimating the parameters
of the eleven mixture models. 2 ) Point estimation of the parameters of two -
parameter Weibull distribution using twelve methods and three - parameter Weibull
distribution using nine methods. 3 ) The Bayesian inference for the three -
parameter Weibull distribution. 4 ) Estimating parameters of the three - parameter
Birnbaum - Saunders, generalized exponential, and Weibull distributions fitted to
grouped data using three methods including approximated maximum likelihood,
expectation maximization, and maximum likelihood. 5 ) Estimating the parameters
of the gamma, log-normal, and Weibull mixture models fitted to the grouped data
through the EM algorithm, 6 ) Estimating parameters of the nonlinear height curve
fitted to the height - diameter observation, 7 ) Estimating parameters, computing
probability density function, cumulative distribution function, and generating
realizations from gamma shape mixture model introduced by Venturini et al. (2008)
<doi:10.1214/07-AOAS156> , 8 ) The Bayesian inference, computing probability
density function, cumulative distribution function, and generating realizations
from four-parameter Johnson SB distribution, 9 ) Robust multiple linear regression
analysis when error term follows skewed t distribution, 10 ) Estimating
parameters of a given distribution fitted to grouped data using method of maximum
likelihood, and 11 ) Estimating parameters of the Johnson SB distribution through
the Bayesian, method of moment, conditional maximum likelihood, and two - percentile
method.

Mahdi Teimouri

ForestFit

Statistical Modelling for Plant Size Distributions

pjsb function

<dl><dt>data</dt>
<dd>Vector of observations.</dd><dt>param</dt>
<dd>Vector of the parameters $\delta$, $\gamma$, $\lambda$, and $\xi$.</dd><dt>log.p</dt>
<dd>If <code>TRUE</code>, then log(cdf) is returned.</dd><dt>lower.tail</dt>
<dd>If <code>FALSE</code>, then <code>1-cdf</code> is returned.</dd></dl>

Arguments

Author

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

<dl>

<dt>data</dt>
<dd>Vector of observations.</dd>

<dt>param</dt>
<dd>Vector of the parameters $\delta$, $\gamma$, $\lambda$, and $\xi$.</dd>

<dt>log.p</dt>
<dd>If <code>TRUE</code>, then log(cdf) is returned.</dd>

<dt>lower.tail</dt>
<dd>If <code>FALSE</code>, then <code>1-cdf</code> is returned.</dd>

</dl>

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

Description

Usage

Value

Arguments

Author

Examples