View Submission - EcoSta2019

A0523
**Title: **Exact one- and two-sample likelihood ratio tests based on type-I and joint type-II censored exponential data
**Authors: **Xiaojun Zhu - Xi'an Jiaotong-Liverpool University (China) **[presenting]**

**Abstract: **The likelihood ratio test is one of the commonly used procedures for hypothesis testing. Several results on likelihood ratio test have been discussed for testing the scale parameter of an exponential distribution under complete and censored data; however, all of them are based on approximations of the involved null distributions. We first derive the exact distribution of the likelihood ratio statistic for testing the scale parameter of an exponential distribution based on a time-constrained life-testing experiment. We also obtain the asymptotic distribution, for the use in large sample size. We then discuss the derivation of its power function. Next, we consider the likelihood ratio test of $\theta_2=\gamma_0*\theta_1$ when data are obtained from two exponential distributions based on a time-constrained life-testing experiment. We derive both exact and asymptotic distributions of the likelihood ratio statistic and then use them to determine the reject region as well as the power function. We then extend the result to the case of Joint Type-II Censored Exponential Data and use the exact power function to design an optimal experiment. Finally, two illustrative examples are presented for demonstrating all the inferential results.