A note on 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 note, 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 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.
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