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The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing

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  • Nowak, Piotr Bolesław

Abstract

This paper refers to the problem stated by Balakrishnan et al. (2002). They proved that maximum likelihood estimator (MLE) of the exponential mean obtained from grouped samples is stochastically ordered provided that the sequence of the successive distances between inspection times is decreasing. In this paper we show that the assumption of monotonicity of the sequence of distances can be dropped.

Suggested Citation

  • Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    • Handle: RePEc:eee:stapro:v:111:y:2016:i:c:p:49-54
    DOI: 10.1016/j.spl.2015.12.029
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    References listed on IDEAS

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    1. 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.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    3. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    4. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    5. Gan, Gaoxiong, 1998. "MLE are stochastically increasing if likelihoods are unimodal," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 289-292, October.
    6. N. Balakrishnan & C. Brain & Jie Mi, 2002. "Stochastic Order and MLE of the Mean of the Exponential Distribution," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 83-93, March.
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