Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

The Pareto distribution, which is originally applied to describe the distribution of wealth in a society, is a power law probability distribution that is used to describe many types of observable phenomena such as social, scientific, geophysical, actuarial phenomena. The power function distribution is a special case of the Pareto distribution. It has applications in finance and economics and is used to model reliability growth of complex systems or reliability of repairable systems. Two new weighted distributions are introduced using the logarithmic weight function. These distributions are the Log-weighted Pareto distribution and the Log-weighted power function distribution. Several statistical properties of these weighted distributions are studied and derived including the cumulative distribution function, location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life, moments, shape indices such as skewness and kurtosis coefficients and order statistics. Moreover, A parametric estimation is performed to obtain estimators for the distributions parameters using three different estimation methods; namely, the maximum likelihood method, the method of moments method and the L-moments method. Numerical simulations are carried out, for both distributions, to validate the robustness of the proposed distributions

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