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.
Highlights
Bivariate distributions are useful for joint modelling and naturally fitting these distributions is a necessity for pricing in insurance and finance
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
We would like to choose the moment conditions so that high efficiencies can be achieved and handle the procedures numerically. We focus on these points for a class of distributions with closed form BLT or BMGF and do not emphasize asymptotic theory in the paper
Summary
Bivariate distributions are useful for joint modelling and naturally fitting these distributions is a necessity for pricing in insurance and finance. New bivariate distributions created using the traditional distribution or survival copulas are often continuous with closed form distribution functions or density functions so that methods based on likelihood functions can be applied for statistical inferences. The BLTPM operator can be used to generate bivariate infinite divisible distributions with closed form BLTs. It appears to be useful to have bivariate infinite divisible distributions for joint modeling as they are related to corresponding bivariate Lévy processes with stationary and independent increments. It appears to be useful to have bivariate infinite divisible distributions for joint modeling as they are related to corresponding bivariate Lévy processes with stationary and independent increments These types of processes are useful as they often lead to elegant results in risk theory in actuarial sciences and in finance. Along the same vein of univariate MEEL methods, bivariate MEEL methods of estimation and tests are based on constraints specified by moments
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
