fitbayesJSB: Estimating parameters of the Johnson's SB (JSB) distribution...
In ForestFit: Statistical Modelling for Plant Size Distributions

fitbayesJSB

R Documentation

Estimating parameters of the Johnson's SB (JSB) distribution using the Bayesian approach

Description

Suppose x=(x_1,\dots,x_n)^T denotes a vector of n independent observations coming from a four-parameter JSB distribution with probability density function given given by

f\bigl(x\big|\Theta\bigr) = \frac {\delta \lambda}{\sqrt{2\pi}(x-\xi)(\lambda+\xi-x)}\exp\Biggl\{-\frac{1}{2}\Bigg[\gamma+\delta\log \biggl(\frac{x-\xi}{\lambda+\xi-x}\biggr) \Bigg]^2\Biggr\},

where \xi<x<\lambda+\xi, \Theta=(\delta,\gamma,\lambda,\xi)^T with \delta, \lambda> 0, -\infty<\gamma<\infty, and -\infty<\xi<\infty. Using the Bayesian approach, we compute the Bayes' estimators of the JSB distribution parameters.

Usage

fitbayesJSB(data, n.burn=8000, n.simul=10000)

Arguments

`data`	Vector of observations.
`n.burn`	Length of the burn-in period, i.e., the point after which Gibbs sampler is supposed to attain convergence. By default `n.burn` is 8000.
`n.simul`	Total numbers of Gibbs sampler iterations. By default `n.simul` is 10,000.

Details

The Bayes' estimators are obtained by averaging on the all iterations between n.burn and n.simul.

Value

A list of objects in two parts as

Bayes' estimators of the parameters.
A sequence of four goodness-of-fit measures consist of Anderson-Darling (AD), Cramer-von Mises (CVM), Kolmogorov-Smirnov (KS), and log-likelihood (log-likelihood) statistics.

Author(s)

Mahdi Teimouri

References

N. L. Johnson, 1949. Systems of frequency curves generated by methods of translation, Biometrika, 36, 149–176.

L. J. Norman, S. Kotz, and N. Balakrishnan, 1994. Continuous Univariate Distributions, volume I, John Wiley & Sons.

Examples


# Here we use the SW dataset provided by FIA that represents a typical loblolly pine plantation.
# As the variable of interest, we fit the JSB distribution to the diameter at breast height (SW$DIA)
# in inches.
data(SW)
data<-SW$DIA
fitbayesJSB(data, n.burn=4000, n.simul=5000)

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