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

Author

Listed:
  • Xiaojun Zhu

    (Xi’an Jiaotong-Liverpool University)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Hon-Yiu So

    (University of Waterloo)

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. 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 $$\theta _2=\gamma _0\theta _1$$ θ 2 = γ 0 θ 1 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.

Suggested Citation

  • Xiaojun Zhu & Narayanaswamy Balakrishnan & Hon-Yiu So, 2022. "Exact One- and Two-Sample Likelihood Ratio Tests based on Time-Constrained Life-Tests from Exponential Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2009-2028, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09907-0
    DOI: 10.1007/s11009-021-09907-0
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    References listed on IDEAS

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    1. S. K. Perng, 1978. "A test for equality of two exponential distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(2), pages 93-102, June.
    2. Xiaojun Zhu & N. Balakrishnan & Yiliang Zhou, 2020. "Exact Likelihood-Ratio Tests for a Simple Step-Stress Cumulative Exposure Model with Censored Exponential Data," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 497-509, June.
    3. N. Balakrishnan & G. Iliopoulos, 2009. "Stochastic monotonicity of the MLE of exponential mean under different censoring schemes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 753-772, September.
    4. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
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