Exact likelihood-ratio tests for joint type-II censored exponential data. (English) Zbl 1441.62071
Given two exponential populations with scale parameters \(\theta_X\) and \(\theta_Y\), and corresponding observations \(X_1,\ldots,X_n\) and \(Y_1,\ldots,Y_m\), respectively, suppose we observe only the \(r\) smallest of these \(m+n\) data points. In this setting, the authors consider the likelihood ratio test for a null hypothesis of the form \(\mbox{H}_0:\theta_Y=\gamma_0\theta_X\) for some given \(\gamma_0\). The exact distribution of the test statistic and power function of the test are derived, and the case where there is a known ordering between \(\theta_X\) and \(\theta_Y\) is considered. The optimal design of this experiment is discussed, and the paper concludes with numerical examples to illustrate the results obtained.
Reviewer: Fraser Daly (Edinburgh)
MSC:
| 62F03 | Parametric hypothesis testing |
| 62E15 | Exact distribution theory in statistics |
| 62N01 | Censored data models |
| 62N05 | Reliability and life testing |
| 62K05 | Optimal statistical designs |
| 62G30 | Order statistics; empirical distribution functions |
Keywords:
exponential distribution; joint type-II censoring; likelihood-ratio test; optimal design; orderingReferences:
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