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.