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Balakrishnan, N. and Lai, C.-D. (2009) Continuous Bivariate Distributions. Second Edition, Springer, New York, Chapter 4.

has been cited by the following article:

• TITLE: Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

  AUTHORS: Andrew Luong

  KEYWORDS: Bivariate Power Mixture Operator, Laplace Transform Copulas, Chi-Square Test Statistics, Bivariate Normality, Infinite Divisibility, Empirical Likelihood

  JOURNAL NAME: Open Journal of Statistics, Vol.8 No.2, April 10, 2018

  ABSTRACT: Maximum Entropy Empirical Likelihood (MEEL) methods are extended to bivariate distributions with closed form expressions for their bivariate Laplace transforms (BLT) or moment generating functions (BMGF) without closed form expressions for their bivariate density functions which make the implementation of the likelihood methods difficult. These distributions are often encountered in joint modeling in actuarial science and finance. Moment conditions to implement MEEL methods are given and a bivariate Laplace transform power mixture (BLTPM) is also introduced, the new operator generalizes the existing univariate one in the literature. Many new bivariate distributions including infinitely divisible(ID) distributions with closed form expressions for their BLT can be created using this operator and MEEL methods can also be applied to these bivariate distributions.