typeIIbs {bibs}

Bayesian estimator for the Birnbaum-Saunders family under progressive type-II censoring scheme.

Description

Estimates parameters of the Birnbaum-Saunders family in a Bayesian framework through the Metropolis-Hasting algorithm when subjects are placed on progressive type-II censoring scheme with likelihood function

l(\alpha,\beta|x_{1:m:n},\dots,x_{m:m:n})=\log L(\Theta) \propto C \sum_{i=1}^{m} \log f(x_{i:m:n}{{;}}|\alpha,\beta) + \sum_{i=1}^{m} R_i \log \bigl[1-F(x_{i:m:n}{{;}}|\alpha,\beta)\bigr],

in which F(.|\alpha,\beta) is cumulative distribution function of the Birnbaum-Saunders family with C=n(n-R_1-1)(n-R_1-R_2-2)\dots (n-R_1-R_2-\dots-R_{m-1}-m+1). The acceptance for each new sample of \alpha and \beta, respectively, becomes

A_{\alpha}=\min \left\{1,\prod_{i=1}^{m}\frac{\bigl[1-F_{BS}(t_{i:m:n}|1/(\alpha^{new})^2,\beta)\bigr]^{R_{i}}}{\bigl[1-F_{BS}(t_{i:m:n}|1/(\alpha_{old})^2,\beta)\bigr]^{R_{i}}}\right\}

,

A_{\beta}=\min \left\{1,\prod_{i=1}^{m}\frac{\bigl[1-F_{BS}(t_{i:m:n}|\alpha,\beta^{new})\bigr]^{R_{i}}}{\bigl[1-F_{BS}(t_{i:m:n}|\alpha,\beta_{old})\bigr]^{R_{i}}}\right\}.

Usage

typeIIbs(plan, M0 = 4000, M = 6000, CI = 0.95)

Arguments

plan

Censoring plan for progressive type-II censoring scheme. It must be given as a data.frame including: number of item placed on the test at time zero and a vector that contains number R, of the removed alive items.

M0

The number of sampler runs considered as burn-in.

M

The number of total sampler runs.

CI

Confidence or coverage level for constructing percentile confidence interval. That is 0.95 by default.

Value

A list including summary statistics after burn-in point including: mean, median, standard deviation, 100(1 - CI)/2 percentile, 100(1/2 + CI/2) percentile.

Author(s)

Mahdi Teimouri

References

M. Teimouri and S. Nadarajah 2016. Bias corrected MLEs under progressive type-II censoring scheme, Journal of Statistical Computation and Simulation, 86 (14), 2714-2726.

N. Balakrishnan and R. Aggarwala 2000. Progressive Censoring: Theory, Methods, and Applications. Springer Science \& Business Media, New York.

Examples

data(plasma)
typeIIbs(plan = plasma, M0 = 100, M = 200, CI = 0.95)