Application to Engineering and Medical Data Using Three-Parameter Exponential Model

Waleed Almutiry,Mohammed Elgarhy,Ibrahim Elbatal,Amani Abdullah Alahmadi,Oluwafemi Samson Balogun,Ibrahim E Ragab,Sikandar Ali

doi:10.1155/2021/9550156

Abstract

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

Highlights

Outliers have less of an impact on the measures Bowley’s skewness (BS) and measure of kurtosis (MK), which exist even for distributions that do not have moments
It is seen that the MREL (Figure 4(a)) is decreasing while the mean inactivity time (MINT) (Figure 4(b)) is increasing
I 1 i 1 i 1 e likelihood equations for the TTLE distribution can with respect to the parameters λ, θ, and α which are offered be managed to obtain by differentiating equation (25) by zLn

Summary

Introduction

Many experts have offered a wide range of methods for including an extra parameter in distributions, and all these new families have been used to describe data from a wide variety of fields, covering engineering, economics, biological studies, environmental sciences, and so on. ese families are created by adding an additional shape parameter to the parent distribution to enhance the capabilities and validity of the data modeling in reality. e statistical literature has demonstrated several new families, the transmuted-G by [1], the logistic-X family by [2], ToppLeone-G (TL-G) by [3], type II half logistic G [4], odd-Burr G by [5], transmuted exponentiated generalized G by [6], Topp-Leone odd Lindley G by [7], odd Frechet G by [8], truncated inverted Kumaraswamy G [9], and truncated Cauchy power G [10], among others. Many experts have offered a wide range of methods for including an extra parameter in distributions, and all these new families have been used to describe data from a wide variety of fields, covering engineering, economics, biological studies, environmental sciences, and so on. Ese families are created by adding an additional shape parameter to the parent distribution to enhance the capabilities and validity of the data modeling in reality. Reference [11] recently published the TTL-G, a distinct family of continuous distributions with the distribution function (cdf ) and density function (pdf ), Mobile Information Systems.

Structural Properties

Reliability Measures

Maximum Likelihood Estimation

Applications