A New Logarithmic Pie Power-G family of Distributions: Properties and Applications to Medical and Traffic Data

Abstract

The present study proposes a new versatile family of distributions, called the New Logarithmic Pie Power-G (NLPP-G) family of probability distributions, applying the Power transformation approach. The newly introduced family of distributions has the ability to enhance the flexibility level of the classical distributions without adding extra parameters. A special subcase of the NLPP-G family, by applying the Inverse Weibull model as a baseline member, is suggested. The subcase of the NLPP-G family is called the New Logarithmic Pie Power Inverse Weibull distribution (NLPP-IWD). The cumulative distribution, survival, probability density, and hazard functions of the NLPP-IWD are investigated graphically. Similarly, for the NLPP-IWD, various range of statistical properties, including moments, moment-generating functions, characteristic functions, incomplete moments, mean residual-life, and order statistics, are derived. Based on the Maximum Likelihood Estimation (MLE) method, we have estimated the unknown parameters of the NLPP-IWD, and its practical performance is verified by the Monte Carlo simulation analysis.  The numerical results and graphical illustration of the Monte Carlo simulation analysis indicated that biases and mean square error decreased as the sample size increased.  Lastly, three are considered to illustrate the practical effectiveness of the NLPP-IWD. The practical performance of the NLPP-IWD is compared with ten well-known distributions using different model selection measures. These evaluations provide empirical evidence that the introduced distribution performs better than ten well-known competing distributions.