Type I Half Logistic Burr X-G Family: Properties, Bayesian, and Non-Bayesian Estimation under Censored Samples and Applications to COVID-19 Data

Ali Algarni,I Elbatal,Amal S Hassan,Abdullah M Almarashi,Abdulkader M Daghistani,Ehab M Almetwally,Mohammed Elgarhy,Naeem Jan

doi:10.1155/2021/5461130

Abstract

In this paper, we present a new family of continuous distributions known as the type I half logistic Burr X-G. The proposed family’s essential mathematical properties, such as quantile function (QuFu), moments (Mo), incomplete moments (InMo), mean deviation (MeD), Lorenz (Lo) and Bonferroni (Bo) curves, and entropy (En), are provided. Special models of the family are presented, including type I half logistic Burr X-Lomax, type I half logistic Burr X-Rayleigh, and type I half logistic Burr X-exponential. The maximum likelihood (MLL) and Bayesian techniques are utilized to produce parameter estimators for the recommended family using type II censored data. Monte Carlo simulation is used to evaluate the accuracy of estimates for one of the family’s special models. The COVID-19 real datasets from Italy, Canada, and Belgium are analysed to demonstrate the significance and flexibility of some new distributions from the family.

Highlights

Statistical researchers have been encouraged in recent years to propose new broad families of continuous univariate distributions and to focus their efforts on improving their desired characteristics
Some of the more recent generators sounding in the literature are the beta–G [1], type I half logistic [2], odd exponentiated half logistic G [3], Marshall–Olkin Burr X-G [4], generalized odd log-logistic-G [5], beta Burr type X − G [6], new generalized odd log-logistic-G [7], generalized Burr X–G [8], type II half logistic [9], the transmuted odd Frechet–G family in [10], Kumaraswamy-type I half logistic [11], and Burr X-exponential-G [12], among others
We looked at the statistical properties of the HLBX − G distribution; Mos, incomplete moments (InMo), mean deviation (MeD), Lo, and Bo curves; ReL and RReL functions; and PrWMs

Summary

Introduction

Statistical researchers have been encouraged in recent years to propose new broad families of continuous univariate distributions and to focus their efforts on improving their desired characteristics. Reference [13] proposed a new simple family of distributions with cumulative distribution function (CDFu) and probability density function (PDFu) using the Burr X as generator; the so-called Burr X − G family is as follows: Mathematical Problems in Engineering. Where g(x; δ) and G(x; δ) are the PDFu and CDFu of any baseline distribution based on a parameter δ. E CDFu and PDFu of the HLBX − G family of distributions are provided by 1−. Half-Logistic Burr X Rayleigh (HLBXR) Distribution e CDFu and PDFu of the HLBXR model (for x > 0) are.

Fundamental Properties

Statistical Inference under Type II Censored Sample

Simulation Results

Conclusion