Mathematics and Statistics Vol. 12(4), pp. 303 - 313
DOI: 10.13189/ms.2024.120401
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Construction of Bivariate Transmuted Frechet Distribution with its Properties

Hayfa Abdul Jawad Saieed , Mhasen Saleh Altalib ^*, Safwan Nathem Rashed , Manaf Hazim Ahmed
Department of Statistics &Informatics, College of Computer Science &Mathematics, University of Mosul, Iraq

ABSTRACT

In multivariate data modeling, the statistical analyst can desire to construct a multivariate distribution with correlated variables. For this reason, there is a need to generalize univariate distributions, but this generalization is not easy. Many methods have been presented for construction of continuous multivariate families with univariate distributions. Some of these methods are based on a single baseline, while others are based on more than one baseline, so that their variables are dependent. Some authors were interested in expanding a univariate transmuted family into multivariate case. Some suggestions were made about extension of univariate quadratic transmuted (QT) family to bivariate ones, and another modification was made to this family by replacing the (c.d.f.) with exponentiated (c.d.f.). Another construction of bivariate family is based on probability distribution of paired order Statistics for a sample size two drawn from quadratic ranked transmuted (QRT) margin, and this bivariate family allows for positive and negative dependence between variables. Another family proposed an extension of univariate mixture of standard continuous uniform, with decreasing densities to a bivariate case. Our proposed (CT₂) reduces to a bivariate quadratic transmuted (QT₂) family if the cubic transmutation parameters equal to zero. (CT₂) family can be used for modeling positive and negative correlated variables. Some statistical properties of (CT₂) family have been studied which comprise joint, marginal and conditional (c.d.f., p.d.f), joint, marginal and conditional moments, data generation and dependence coefficients. It is seen that (joint, marginal and conditional) moments depend on raw moments of (baseline variables and largest order statistics of samples sizes 2 and 3). The Egyptian bivariate economic data are fitted by (CT₂Fr), (FGMFr), (T₂Fr) and (DSASFr). The (CT₂Fr) is the fit to which has smallest (AIC) and (BIC) criteria.

KEYWORDS
Frechet Distribution, K-transmuted Family, Bivariate Quadratic Family, Bivariate Cubic Transmuted Family, Bivariate T-X Family, Two-stage Maximum Likelihood Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Hayfa Abdul Jawad Saieed , Mhasen Saleh Altalib , Safwan Nathem Rashed , Manaf Hazim Ahmed , "Construction of Bivariate Transmuted Frechet Distribution with its Properties," Mathematics and Statistics, Vol. 12, No. 4, pp. 303 - 313, 2024. DOI: 10.13189/ms.2024.120401.

(b). APA Format:
Hayfa Abdul Jawad Saieed , Mhasen Saleh Altalib , Safwan Nathem Rashed , Manaf Hazim Ahmed (2024). Construction of Bivariate Transmuted Frechet Distribution with its Properties. Mathematics and Statistics, 12(4), 303 - 313. DOI: 10.13189/ms.2024.120401.