Journal of Data Science

The Power function distribution is a flexible life time distribution that has applications in finance and economics. It is, also, used to model reliability growth of complex systems or the reliability of repairable systems. A new weighted Power function distribution is proposed using a logarithmic weight function. Statistical properties of the weighted power function distribution are obtained and studied. Location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life are derived. Shape indices such as skewness and kurtosis coefficients and order statistics are obtained. Parametric estimation is performed to obtain estimators for the parameters of the distribution using three different estimation methods; namely: the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution.

In this paper, we considered a new generalization of the paralogistic distribution which we called the three-parameter paralogistic distribution. Some properties of the new distribution which includes the survival function, hazard function, quantile function, moments, Renyi entropy and the maximum likelihood estimation (MLE) of its parameters are obtained. A simulation study shows that the MLE of the parameters of the new distribution is consistent and asymptotically unbiased. An applicability of the new three-parameter paralogistic distribution was subject to a real lifetime data set alongside with some related existing distributions such as the Paralogistic, Gamma, Transformed Beta, Log-logistic and Inverse paralogistic distributions. The results obtained show that the new three-parameter paralogistic distribution was superior to other aforementioned distributions in terms of the Akaike information criterion (AIC) and K-S Statistic values. This claim was further supported by investigating the density plots, P-P plots and Q-Q plots of the distributions for the data set under study.