A a Type Ii Half Logistic Exponentiated-G Family of Distributions With Applications to Survival Analysis

Abstract

Statisticians have created and proposed new families of distribution by extending or generalizing existing distributions. These families of distributions are made more flexible in fitting different types of data by adding one or more parameters to the baseline distributions. In this article, we present a new family of distributions called Type II half-logistic exponentiated-G family of distributions. We discuss some of the statistical properties of the proposed family such as explicit expressions for the quantile function, probability weighted moments, moments, generating function, survival and order statistics. The new family’s sub-models were discussed. We discuss the estimation of the model parameters by maximum likelihood. Two real data sets were employed to show the usefulness and flexibility of the new family

The properties of Type II Half-Logistic Exponentiated Weibull Distribution with Applications

“…Using the family of distributions proposed by Bello et al, (2021), we developed and investigated a novel distribution in this study known as the Type II Half-Logistic Exponentiated Weibull Distribution. As statistical elements of the new proposed distribution, explicit quantile function, probability weighted moments, moments, generating function, reliability function, hazard function, and order statistics were investigated.…”

“…Mudholkar et al, (1996) pioneered Exponentiated Weibull distribution, the modified Weibull extension by Xie et al, (2002) , flexible Weibull extension (FWEx) by Bebbington et al,(2007), beta modified Weibull by Silva et al, (2010), Kumaraswamy Weibull by , transmuted Weibull by Aryal and Tsokos (2011), truncated Weibull distribution by Zhang and Xie (2011), Kumaraswamy inverse Weibull by Shahbaz et al,(2012), exponentiated generalized Weibull by Cordeiro et al,(2013), McDonald modified Weibull by Merovci and Elbatal (2013), beta inverse Weibull by Hanook et al,(2013), transmuted additive Weibull by Elbatal and Aryal (2013), McDonald Weibull by Cordeiro et al,(2014), Kumaraswamy modified Weibull by Cordeiro et al,(2014), transmuted complementary Weibull geometric by Afify et al,(2014), Kumaraswamy transmuted exponentiated additive Weibull by Nofal et al,(2016), generalized transmuted Weibull by Nofal et al,(2017), Topp-Leone generated Weibull by Aryal et al,(2017), Kumaraswamy complementary Weibull geometric by Afify et al,(2017), Marshall-Olkin additive Weibull by Afify et al,(2018), Zubair-Weibull by Ahmad (2018), alpha power transformed Weibull by , Topp Leone exponentiated weibull by Ibrahim (2021) distributions. Bello et al, (2021) propound a new distribution family called the Type II Half-Logistic Exponentiated-G (TIHLEt-G) with two extra shape parameters. For any arbitrary cumulative distribution function as a baseline (cdf) , the TIIHLEt-G family with two positive shape parameters and has cumulative distribution function (cdf) and probability density function (pdf) given by: https://scientifica.umyu.edu.ng/…”

“…According to Bello et al, (2021), the TIIHLEt-G distribution family has various characteristics that distinguish it from traditional distribution models. One such characteristic is its increased flexibility with regards to kurtosis, which can result in more accurately fitting the distribution to real data.…”

“…The Type II half logistic Weibull (TIIHLEtW) distribution is the name given to the new model. We generate the TIIHLEtW distribution from Bello et al, (2021) and provide some essential statistical properties.…”

On the Properties of Topp-Leone Kumaraswamyweibul Distribution With Applications to Biomedical Data

“…In statistical distribution theory, researchers are in the quest to generate new distributions by adding more parameters to the classical distributions in order to make them more robust, versatile and flexible in fitting different kinds of data. Some new ideas of generalizing probability distributions can be found in Beta-G family due to Eugene et al, (2002), Transmuted-G family due to (Shaw & Buckley, 2007), gamma-G family due to (Zografos & Balakrishanan, 2009), Kumaraswamy-G family due to (Cordeiro & de Castro 2011), McDonald-G family due to (Alexander et al, 2012), T-X family due to (Alzaatreh et al, 2013), the exponentiated T-X family due to (Alzaghal et al, 2013), the Weibull-G family due to (Bourguignon et al, 2014), a quantile based T-XY approach due to (Aljarrah et al, 2014), the logistic-G family due to (Tahir et al, 2016), Topp-Leone-G due to (Al-Shomrani et al,, 2016), Topp-Leone Expononentiated-G family due to (Ibrahim et al,, 2020a), Type I Half Logistic Exponentiated-G family due to (Bello et al, 2020), Type II Half Logistic Exponentiated-G family due to (Bello et al, 2021), extended Topp-Leone exponentiated generalized-G family due to (Sule et al, 2022). The Weibull distribution is a very popular model and has been extensively used over the past decades for modeling data in reliability, engineering and biological studies.…”