Abstract
Abstract The Pareto distribution satisfies the power law, which is widely used in physics, biology, earth and planetary sciences, economics, finance, computer science, and many other fields. In this article, the logarithmic Pareto distribution, a logarithmic transformation of the Pareto distribution, is presented and studied. The moments, percentiles, skewness, kurtosis, and some dynamic measures such as hazard rate, mean residual life, and quantile residual life are discussed. The parameters were estimated by quantile and maximum likelihood methods. A simulation study was conducted to investigate the efficiency, consistency, and behavior of the maximum likelihood estimator. Finally, the proposed distribution was fitted to some datasets to show its usefulness.
Highlights
The Pareto distribution, a power law model, is useful in analyzing observations from physics, biology, earth and planetary sciences, economics, finance, computer science, social science, geophysics, actuarial science, quality control, and many other fields [1].The Pareto model can be applied in situations where there is an equilibrium in the distribution of “small” to “large” values
There are many such cases, e.g., the size of files transmitted over the Internet network TCP/IP consisting of many small and few large files, the error rates of hard disks consisting of many small and few large error rates, the size of human settlements consisting of many small values for hamlets/villages and few large values for cities, and the oil reserves in oil fields consisting of many small and few large fields
It does not imply that parameter values are well captured. It is possible for the fitted parameter values to deviate from the true parameter values very substantially, while the fitted cumulative distribution function (CDF) is close to the CDF of data
Summary
The Pareto distribution, a power law model, is useful in analyzing observations from physics, biology, earth and planetary sciences, economics, finance, computer science, social science, geophysics, actuarial science, quality control, and many other fields [1]. The Pareto model can be applied in situations where there is an equilibrium in the distribution of “small” to “large” values. There are many such cases, e.g., the size of files transmitted over the Internet network TCP/IP consisting of many small and few large files, the error rates of hard disks consisting of many small and few large error rates, the size of human settlements consisting of many small values for hamlets/villages and few large values for cities, and the oil reserves in oil fields consisting of many small and few large fields. Ihtisham et al [10] provided the power transformation of the single-parameter Pareto distribution. We apply the logarithmic transformation to the Pareto distribution. The aim of this article is to present and study a logarithmic transformation of the Pareto distribution.
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