A class of power inverted Topp-Leone distribution: Properties, different estimation methods & applications

The power inverted Topp Leone power series (PITLPS) class is a novel three-parameter version of the power inverted Topp Leone (PITL) distribution. The PITLPS class is created by combining a power series distribution with the PITL distribution. This compounding process allows for the creation of flexible classes of distributions with strong physical interpretations in fields such as biology and engineering. The PITLPS class has a number of different hazard rate shapes. This class includes some novel lifetime distributions as well as a new compound class. The formula for the density function, limiting behaviour, moments and incomplete moments, and the Renyi entropy measure are all examined as important distributional features. Furthermore, for one elective model, five distinct estimating approaches are considered. To compare the performance of various estimates, a simulation analysis of the PITL Poisson distribution as a one sub-model is provided. In-depth simulation results have been arranged using partial and overall ranks to find the best estimation technique. Finally, the PITL Poisson model is applied to three real data sets, and the fit is compared to that of some other well-known distributions for explanatory purposes. The proposed model is seen to have certain advantages in interpreting lifetime data when compared to other common models in that it has more shapes and flexibility than many already existing distributions.