Abstract
In this article a new bivariate distribution, whose both the marginals are finite mixture of gamma distribution has been defined. Several of its properties such moments, correlation coefficients, measure of skewness, moment generating function, Renyi and Shannon entropies have been derived. Simulation study have been conducted to evaluate the performance of maximum likelihood method.
Highlights
The univariate gamma distribution is one of the most commonly used statistical distributions to analyze skewed data in many disciplines and has been studied extensively in scientific literature
The chi-square distribution, which is of utmost importance in statistical inference, is a special case of gamma distribution
The univariate gamma distribution has been generalized to the bivariate case in many different ways and many forms of bivariate gamma distribution are available
Summary
The univariate gamma distribution is one of the most commonly used statistical distributions to analyze skewed data in many disciplines and has been studied extensively in scientific literature. Nadarajah [15], by using two independent gamma variables, constructed a bivariate distribution which has gamma and beta distributions as its marginals. We introduce a bivariate gamma distribution whose marginals are finite mixtures of gamma distributions and study its properties. This is the first bivariate distribution of its kind and is suitable for bivariate data with negative correlation. In the last section, simulation study is conducted to evaluate the performance of maximum likelihood method
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