A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation, and Applications

Alya Al Mutairi,Badr Alnssyan,Muhammad Z Arshad,Hazem Al-Mofleh,Muhammad Z Iqbal,Ahmed Z Afify

doi:10.3390/math9172024

Abstract

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

Highlights

The basic aim to carry out the present study is to develop a flexible bathtub-shaped failure rate model called the exponentiated new power function (E-NPF) distribution, which has some useful properties such as (i) its cumulative distribution function (CDF), probability density function (PDF), and likelihood function are simple and easy to interpret; (ii) from the application perspective, this model is quite uncomplicated; (iii) its density and failure rate shapes follow the skewed and bathtub shapes; and (iv) this model provides a consistently better fit over its competitors
The E-NPF distribution is compared with its competing models, which are present in Table 8, based on some criteria such as the Akaike information criterion (AIC), Cramér–von Mises (CM), Anderson–Darling (AD), and Kolmogorov–Smirnov (KS)
We develop a bounded lifetime model that exhibits a bathtub-shaped

Summary

Introduction

Over the past three decades, the promising attention of researchers towards the development of new generalized models has increased to explore the hidden characters of baseline models. New generalized models open new horizons to address real-world problems and to provide an adequate fit to the complex and asymmetric random phenomena. Various models have been constructed and studied in the literature. One of the simplest and most handy lifetime models induced in the statistical literature is the Lehmann Type I (L-I) and Type II models [1]. The L-I model is most often discussed in favor of the power function (PF) distribution. The L-I model is the exponentiation of any baseline model, and it can be specified by the following cumulative distribution function (CDF): distributed under the terms and

Methods

Results

Conclusion