mlebs {bibs}

Computing the maximum likelihood (ML) estimator for the generalized Birnbaum-Saunders (GBS) distribution.

Description

Computing the ML estimator for the GBS distribution proposed by Owen (2006) whose density function is given by

f_{{GBS}}(t|\alpha,\beta,\nu)=\frac{(1-\nu)t +\nu \beta}{\sqrt{2\pi}\alpha \sqrt{\beta}t^{\nu+1}} \exp\left\{-\frac{(t-\beta)^2}{2\alpha^2\beta t^{2\nu}}\right\},

where t>0. The parameters of GBS distribution are \alpha>0, \beta>0, and 0<\nu<1. For \nu=0.5, the GBS distribution turns into the ordinary Birnbaum-Saunders distribution.

Usage

mlebs(x, start, method = "Nelder-Mead", CI = 0.95)

Arguments

x

Vector of observations.

start

Vector of the initial values.

method

The method for the numerically optimization that includes one of CG,Nelder-Mead, BFGS, L-BFGS-B, and SANN.

CI

Confidence level for constructing asymptotic confidence intervals. That is 0.95 by default.

Value

A list including the ML estimator, goodness-of-fit measures, asymptotic 100(1-\alpha)\% confidence interval (CI) and corresponding standard errors, and Fisher information matix.

Author(s)

Mahdi Teimouri

Examples

data(fatigue)
x <- fatigue
mlebs(x, start = c(1, 29), method = "Nelder-Mead", CI = 0.95)