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On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

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  • Jin Xia
  • Jie Mi
  • YanYan Zhou

Abstract

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

Suggested Citation

  • Jin Xia & Jie Mi & YanYan Zhou, 2009. "On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-16, September.
    • Handle: RePEc:hin:jnljps:310575
    DOI: 10.1155/2009/310575
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    Cited by:

    1. Broderick O. Oluyede & Boikanyo Makubate & Adeniyi F. Fagbamigbe & Precious Mdlongwa, 2018. "A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications," Stats, MDPI, vol. 1(1), pages 1-15, June.

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