It is well-known that maximum likelihood (ML) estimators of the two parameters in a Gamma distribution do not have closed forms. This poses difficulties in some applications such as real-time signal processing using low-grade processors. The Gamma distribution is a special case of a generalized Gamma distribution. Surprisingly, two out of the three likelihood equations of the generalized Gamma ...

The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory: and Hamilton-Jacobi partial differential equations. We pay the main attention to com...

RESEARCH DESIGN AND METHODSdIn this retrospective cohort study, we compared 18,990 first-attack AP with diabetes to 37,980 matched control subjects from Taiwan’s National Health Insurance Research Database between 2000 and 2009. Primary outcomes were development of severe AP, defined by a modified Atlanta classification scheme, and hospital mortality. Analyses were performed using univariable a...

The generalized empirical likelihood (GEL) method produces a class of estimators of parameters defined via general estimating equations. This class includes several important estimators, such as empirical likelihood (EL), exponential tilting (ET), and continuous updating estimators (CUE). We examine the information geometric structure of GEL estimators. We introduce a class of estimators closel...

A new information-based approach for estimating systems of many equations with nonnegativity constraints is presented. This approach, called generalized maximum entropy (GME), is more practical and efficient than traditional maximum likelihood methods. The GME method is used to estimate an almost ideal demand system for five types of meat using cross-sectional data from Mexico, where most house...

A generic random effects formulation for the Dirichlet negative multinomial distribution is developed together with a convenient regression parameterization. A simulation study indicates that, even when somewhat misspecified, regression models based on the Dirichlet negative multinomial distribution have smaller median absolute error than generalized estimating equations, with a particularly pr...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...