On the unit Burr-XII distribution with the quantile regression modeling and applications

Abstract

In this paper, we modify the Burr-XII distribution through the inverse exponential scheme to obtain a new two-parameter distribution on the unit interval called the unit Burr-XII distribution. The basic statistical properties of the newly defined distribution are studied. Parameters estimation is dealt and different estimation methods are assessed through two simulation studies. A new quantile regression model based on the proposed distribution is introduced. Applications of the proposed distribution and its regression model to real data sets show that the proposed models have better modeling capabilities than competing models. Keywords Probability weighted moments IntroductionSeveral unit distributions have been used for modelling data for percentage and proportions in many areas such as biological studies, mortality and recovery rates, economics, health, risks, and measurements sciences. No doubt that the beta, Johnson S B (see Johnson 1949) and Kumaraswamy (see Kumaraswamy 1980) distributions quickly come to the mind, both to model and to obtain inferences based on data sets from the above areas. However, these classical models may be inadequate, which pose many significant problems for accurate data Communicated by Clémentine Prieur.

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

“…[25] introduced the Kumaraswamy quantile regression model for the dependent variables on the (0, 1) interval. The presented idea in the study of [25] has been applied to different probability distributions by [9,11,12,14,[26][27][28][29].…”

“…Similarly, [8] used X = T/(T + 1) transformation on the improved second-degree Lindley (ISDL) distribution and resulting distribution was called as unit-ISDL distribution. These approaches have been used many authors such as [9][10][11][12][13][14][15][16][17][18][19] and so on.…”

A new quantile regression for the COVID-19 mortality rates in the United States

“…The proposal is based on the transformation , where X is a BXII random variable having cumulative distribution function (cdf) and probability density function (pdf) and respectively, where and are shape parameters. It is worth noting that Z can also be seen as a reflected transformation on W , , where W is a random variable following a unit Burr XII (UBXII) distribution pioneered by Korkmaz and Chesneau ( 2021 ). Hence, the cdf and pdf of the reflected unit Burr XII (RUBXII) distribution can be expressed as (for ) and respectively.…”

Parameter Estimation Methods and Applications of the Power Topp-Leone Distribution

“…However, besides TL distribution there exist several unit distributions proposed recently by many researchers including; unit Johnson SU distribution [17], unit generalized half normal distribution [18], logit slash distribution [19], truncated power Lomax distribution [20], and unit Burr-XII distribution [21]. So, the main aim here is to provide a new unit model related to the TL with an extra shape parameter, the so-called PTL distribution using the transformation, 1 , TZ  = where Z has TL distribution.…”