A Lagrangian Non Central Negative Binomial Distribution of the First Kind

作者：Imoto Tomoaki^*; Ong Seng Huat

来源：Communications in Statistics - Theory and Methods, 2013, 42(3): 466-477.

DOI：10.1080/03610926.2011.582564

• Consul distribution
• Dispersion
• Geeta distribution
• Generalized distribution
• Goodness-of-fit
• Lagrangian probability distribution of the first kind
• Mixture
• Queueing theory

A Lagrangian probability distribution of the first kind is proposed. Its probability mass function is expressed in terms of generalized Laguerre polynomials or, equivalently, a generalized hypergeometric function. The distribution may also be formulated as a Charlier series distribution generalized by the generalizing Consul distribution and a non central negative binomial distribution generalized by the generalizing Geeta distribution. This article studies formulation and properties of the distribution such as mixture, dispersion, recursive formulas, conditional distribution and the relationship with queuing theory. Two illustrative examples of application to fitting are given.

• 出版日期2013-2-1