A fully parametric family of distributions called the new generalized family (NGF) is proposed. The cumulative distribution function of the proposed NGF is constructed based on the reciprocal of the hazard rate function. Furthermore, a special sub-family called the new generalized Pareto (NGP) family is also addressed. A special sub-model of the NGP class called the new Kumaraswamy Pareto (NKP) distribution is introduced. The NKP model provides flexible shapes for its hazard and density functions. The properties of the NKP distribution are derived. In addition, the inferences under complete and bootstrapped samples of the NKP parameters are addressed. Monte Carlo simulation studies are also performed to explore the behavior of different estimators. Three real-life datasets are fitted using the NKP distribution, showing the superiority fit of the proposed statistical model.

In statistical modeling, lifetime datasets play an important and significant role. Weighted distributions can be useful to attain the essential purposes relating to the developed distributions’ flexibility and to improve further compliances in data forming; they provide the extension of distributions. The current study suggests a new best-fit probability distribution model based on Pareto distribution. The new model is called Survival Weighted Pareto (SWP) distribution model. Furthermore, the statistical expressions for different properties, which include moments, inverse moments, quantile function, and order statistics, are reported. Moreover, to check the performance and the behavior of different estimators using different sample sizes, a simulation study, which is based on SWP distribution, is performed. According to the simulation results, it is established that the proposed model is a most useful fitted probability model. In addition, an application of the SWP model for three datasets is provided to check the goodness of fit measures of the model.

This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.