An analysis of the maximum likelihood estimates for the Lomax distribution
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The Lomax distribution is a popularly used heavy-tailed distribution that has applications in actuarial sciences. reliability, operations research, income and wealth distributions among many others. But the analytical behavior of the maximum likelihoods for the Lomax distribution is anomalous and it causes difficulty in real-life application of the model for practical purposes. In this work, we provide precise arguments for the anomalous behavior of the log-likelihood surface of the Lomax distribution. A relative variability measure, namely the coefficient of variation (CV) is introduced to characterize the profile log-likelihood of the Lomax distribution. A sufficient condition for the existence of the global maximum of the maximum likelihood estimates and asymptotic results for statistical inferences are also discussed in this paper. An application on a reliability dataset describes the practical relevance of these results.
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