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

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.

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

“…Varian and Savage [ 9 ] presented a highly useful asymmetric loss function, which has lately been employed in different works [ 10 , 11 ] and [ 12 ]. This function is known as the LINEX loss function, according to linear exponentially.…”

A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data

“…Power outages can also be triggered by wildlife and tree branches hitting power cables. This data set is obtained from [29] the power failures' lengths measured in minutes: 22,18,135,15,90,78,69,98,102,83,55,28,121,120,13,22,124,112,70,66,74,89,103,24,21,112,21,40,98,87,132,115,21,28,43,37,50,96,118,158,74,78,83,93,95. We have also grouped the data with the help of the bins code of the R computational package, where possible classes with respective frequencies are enlisted as [13, 22.7], [22.7, 53.3], [53.3, 78] 20 and 21).…”

“…This phenomenon of adding parameters innovates more robust families of distributions, which are being effectively used for modeling engineering, economics, biological studies and environmental sciences data sets. Therefore, in this regard, some famous classes are the Marshall Olkin-G by [1], beta-G by [2], the Kumaraswamy-G studied by [3], odd Fréchet-G by [4] logistic-G by [5], exponentiated generalized-G proposed by [6], odd generalized N-H-G by [7], T -X class by [8], transmuted odd Fréchet-G by [9], exponentiated power generalized Weibull power series-G by [10], the Weibull-G by [11], the exponentiated half-logistic generated family by [12], Type II half logistic class by the odd [13], bivariate Weibull-G family by [14], exponentiated generalized alpha power family of distributions by [15], truncated Cauchy power Weibull-G class of distributions by [16], odd Perks-G class of distributions by [17], Type I half logistic Burr X-G family by [18], sine Topp-Leone-G family of distributions by [19], exponentiated version of the M family of distributions by [20], a new power Topp-Leone generated family of distributions by [21], truncated inverted Kumaraswamy generated family of distributions by [22], generalized exponential class discussed by [23], the beta odd log-logistic generalized studied by [24], alpha power transformation family of distributions introduced by [25], the Kumaraswamy exponential Pareto proposed by [26], the generalized Burr XII power series(GBXIIPS) class studied by [27], additive Weibull geometric (AWG) distribution proposed by [28] and the beta exponentiated modified Weibull (BEMW) distribution developed by [29], among others. However, in recent years, Ref.…”

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“…In recent years, many various of statisticians have been attracted by create new families of distributions for example; exponentiated generalized-G in [1], logarithmic-X family of distributions [2], sine-G in [3], odd Perks-G in [4], odd Lindley-G in [5], truncated Cauchy power-G in [6], truncated Cauchy power Weibull-G-G in [7], Topp-Leone-G in [8], odd Nadarajah-Haghighi-G in [9], the Marshall-Olkin alpha power-G in [10], T-X generator studied in [11], type I half-logistic Burr X-G in [12], KM transformation family in [13], (DUS) transformation family in [14], arcsine exponentiated-X family in [15], Marshall-Olkin odd Burr III-G family in [16], among others.…”