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MAXIMUM LIKELIHOOD ESTIMATION AND PREDICTION OF THE BIVARIATE AND TRIVARIATE EXPONENTIATED INVERTED KUMARASWAMY MODELS
Keywords:
exponentiated distributions, bivariate exponentiated inverted Kumaraswamy model, trivariate exponentiated inverted Kumaraswamy model, Marshall-Olkin method, joint hazard function, maximum likelihood estimators and prediction, Monte Carlo simulationDOI:
https://doi.org/10.17654/0972361725072Abstract
In recent years, the inverted Kumaraswamy distribution has proven to be highly effective for modeling various types of lifetime data. This paper aims to develop a bivariate inverted Kumaraswamy distribution whose marginal distributions follow the inverted Kumaraswamy form. To achieve this, an approach analogous to the Marshall-Olkin method is employed in constructing the bivariate exponential distribution, as it offers a natural and suitable framework. Several key properties are investigated, including the bivariate probability density function and its marginals, as well as the joint reliability and joint hazard functions. Both the joint probability density function and the joint cumulative distribution function are derived in closed form. Parameter estimation for the bivariate and trivariate exponentiated inverted Kumaraswamy models is performed using the maximum likelihood method, and the corresponding approximate variance-covariance matrix is obtained. Additionally, maximum likelihood prediction is addressed. The study concludes with a comprehensive simulation analysis and an application to real-world datasets, demonstrating the practical utility of the proposed models.
Received: August 14, 2025
Accepted: September 13, 2025
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