Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

Waleed Almutiry,Naeem Jan

doi:10.1155/2021/1980480

Abstract

This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research.

Highlights

Length-biased exponential (LBE) or moment exponential (ME) distribution is considered as one of the most important univariate and parametric models
Ere is much to be said for a flexible lifespan distribution model, and this one may be a suitable fit for some sets of failure data
Assume T(1), T(2), . . . , T(n) are the recorded type II censored samples (TIICS) of size r, whose lifetimes have the inverted length-biased exponential (ILBE) distribution with PDF (4), and the experiment is completed once the r-th object fails for just some fixed values of r. e log-likelihood function (LLF), according to TIIC, is provided by ln l2 ln C + 2r ln α −

Summary

Introduction

Length-biased exponential (LBE) or moment exponential (ME) distribution is considered as one of the most important univariate and parametric models. It is commonly utilized in the analysis of data collected throughout a lifespan and in problems connected to the modeling of failure processes. Our motivation here is (i) introducing a new distribution, referred to as the inverted length-biased exponential (ILBE), (ii) studying some of the main properties, (iii) providing point and interval estimators for the model parameter from complete and censored samples, and (iv) examining its applicability using three real datasets.

Fundamental Mathematical Properties of ILBE Distribution

Statistical Inference

Applications to Real Data