Properties of Lagrangian distributions

Abstract

Lagrange’s expansion is the power series expansion of the inverse function of an analytic function, and it leads to general Lagrangian distributions of the first kind as well as of the second kind. We present some theorems in which different sets of two analytic functions provide a Lagrangian distribution. Potential applicability of the theorem to tandem queueing process is studied.

Keywords:

• Generalized negative binomial distribution
• Lagrange’s expansion
• Lagrangian non central negative binomial distribution
• Tandem queue

Mathematics Subject Classification:

• 60E05