TY - JOUR

T1 - Exact One- and Two-Sample Likelihood Ratio Tests based on Time-Constrained Life-Tests from Exponential Distributions

AU - Zhu, Xiaojun

AU - Balakrishnan, Narayanaswamy

AU - So, Hon Yiu

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/9

Y1 - 2022/9

N2 - 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. In this paper, 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, which is useful in the case of a large sample size. We then discuss the derivation of its power function. Next, we consider the likelihood ratio test of θ2= γθ1 when data are obtained from two exponential distributions based on a time-constrained life-testing experiment. Here again, 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. Monte Carlo simulations are then carried out to evaluate the performance of the inferential methods developed here. Finally, some examples are used to illustrate all the inferential results.

AB - 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. In this paper, 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, which is useful in the case of a large sample size. We then discuss the derivation of its power function. Next, we consider the likelihood ratio test of θ2= γθ1 when data are obtained from two exponential distributions based on a time-constrained life-testing experiment. Here again, 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. Monte Carlo simulations are then carried out to evaluate the performance of the inferential methods developed here. Finally, some examples are used to illustrate all the inferential results.

KW - Asymptotic distribution

KW - Exact distribution

KW - Exponential distribution

KW - Likelihood ratio test

KW - Time-constrained life-testing experiment

UR - http://www.scopus.com/inward/record.url?scp=85117726127&partnerID=8YFLogxK

U2 - 10.1007/s11009-021-09907-0

DO - 10.1007/s11009-021-09907-0

M3 - Article

AN - SCOPUS:85117726127

SN - 1387-5841

VL - 24

SP - 2009

EP - 2028

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 3

ER -