A method of constructing test for the parameter of family of lifetime distributions under Type-II censored sample

Abstract

This study considers method of constructing tests for the hypothesis on parameter $\beta \mathrm{ }$of a family of lifetime distributions under type-II censored sample. We propose three test statistics $Q_{\left(\mathit{sd}\right)},$ F and${ Q}_1.$ The performance of these statistics, in terms of power, is studied through simulation for different values of parameter of Burr-XII distribution, log-bathtub distribution, Weibull distribution, and two-parameter exponential distribution. The percentile points and powers for testing the parameter$\mathrm{ }\beta ,$ in each of these distributions, are simulated. For these distributions, the test based on quadratic form $({i.e.Q}_{\left(\mathit{sd}\right)}\mathrm{ }$and${ Q}_1)$performs better than the test F in identifying $\beta >{\beta }_0$ or $\beta <{\beta }_0$ alternatives for some member of the family of distributions. One numerical example is also given.

Keywords:

• Conditional test
• type-II censoring scheme
• conditional distribution
• sufficient statistic
• nuisance parameter
• quadratic form
• power of the test