So, we introduced and thoroughly explored a bivariate extension of a unit distribution, known as the bivariate unit-power Weibull distribution (BIUPWD for short) as far as no bivariate extension has been explored for the unit distributions in the literature. We specify it as follows: (i) we employed a unique transformation to develop UPWD instead of employing traditional transformation found in literature to propose unit distributions which include, , or, depending upon the functional identifiability of the baseline model (ii) recent developments in distribution theory have shown a significant rise in the analysis of bivariate extensions of univariate models for further information, we may refer the readers to see in. The following points provide sufficient incentive to study the proposed model. The fundamental goal of the article under consideration is to introduce a new unit-power Weibull distribution (UPWD for short) as well as to investigate its statistical characteristics. The most valuable unit distributions with a given set of parameters are Johnson, Topp-Leone distribution, unit-Weibull distribution, unit-Gamma distribution, unit-Gompertz distribution, unit-inverse Gaussian distribution, unit-Lindley distribution, unit-generalized half normal distribution, unit-modified Burr-III distribution, unit-Chen distribution, unit-Rayleigh distribution, unit power-logarithmic distribution and unit Nadarajah and Haghighi. Many unit distributions as alternatives to these distributions are presented in the literature to meet this prerequisite. Although the Beta distribution and Kumaraswamy distribution are most widely used models for modeling data sets on the interval, neither the beta distribution holds closed form expressions of cumulative distribution function nor Kumaraswamy distribution holds closed form expressions of moments. For adequate modeling of these variables, continuous probability distributions with support of also known as unit distributions are essential. Variables like proportions of a certain attribute, comparing prices of a grocery item, profit or loss in a business, checking an ability for a job, likes or dislikes about the product of a company, and rates set on the interval (0,1) are frequently encountered in metrology, biological studies, economics, and other sciences. Many disciplines of applied science deal with the constraints of bounded variables measuring specific features of phenomena. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. The real data applications are carried out to underline the practical usefulness of the model. Additionally, several actuarial measures are computed. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, -moments, TL-moments, Rényi entropy, and MLE estimation. In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution.
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