Distribuição normal de Kumaraswamy bivariada

Abstract

The normal distribution is the most important probability distribution, used in modeling of continuous data. However, there are cases where the assumption of distribution related to normal model is violated and the search for other distributions that model these cases is necessary. One of the points that can justify the absence of normality is the lack of symmetry. A distribution whose main characteristic shape asymmetric behavior data is Kumaraswamy. The combination of the flexibility of the modeling asymmetric data distribution Kumaraswamy with known distributions, such as normal andWeibull, enabled the creation of a family of generalized distributions. The multivariate distributions we highlight the importance of applications in data modeling in various field of knowledge. However, there is the existence of few distributions that model heavier tails and asymmetry situations. This study aimed to study the class of generalized distributions Kumaraswamy deduct the normal distribution bivariate Kumaraswamy, present the likelihood function and the expressions of their estimators. Implemented the estimation procedure using the scores functions in textit software R and a simulation approach. We evaluated the simulated data estimation and also in real application examples with asymmetric distribution. It can be concluded therefore that the normal distribution bivariate Kumaraswamy was deduced in relation to their joint density function, marginal, conditional and implemented for the simulation study. The estimators behaved precisely, consistent and unbiased. The normal distribution bivariate Kumarawamy adjusted satisfactorily to the actual data of average temperature and total precipitation.