pgsm

Computes cumulative distribution function (cdf) of the gamma shape mixture (GSM) model. The general form for the cdf of the GSM model is given by
$$F(x,{\Theta}) = \sum_{j=1}^{K}\omega_j F(x,j,\beta),$$
where
$$F(x,j,\beta) = \int_{0}^{x} \frac{\beta^j}{\Gamma(j)} y^{j-1} \exp\bigl( -\beta y\bigr) dy,$$
in which $\Theta=(\omega_1,\dots,\omega_K, \beta)^T$ is the parameter vector and known constant $K$ is the number of components. The vector of mixing parameters is given by $\omega=(\omega_1,\dots,\omega_K)^T$ where $\omega_j$s sum to one, i.e., $\sum_{j=1}^{K}\omega_j=1$. Here $\beta$ is the rate parameter that is equal for all components.

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

pgsm function

<dl><dt>data</dt>
<dd>Vector of observations.</dd><dt>omega</dt>
<dd>Vector of the mixing parameters.</dd><dt>beta</dt>
<dd>The rate parameter.</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 cumulative distribution function of the gamma shape mixture model — pgsm

<dl>

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

<dt>omega</dt>
<dd>Vector of the mixing parameters.</dd>

<dt>beta</dt>
<dd>The rate parameter.</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>

pgsm: Computing cumulative distribution function of the gamma shape mixture model

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