bibs (version 1.1.1)

mlebs: 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.

Examples

# NOT RUN {
data(fatigue)
x <- fatigue
mlebs(x, start = c(1, 29), method = "Nelder-Mead", CI = 0.95)
# }