R-distribution and its applications

Abstract

An R-distribution (RD) is introduced in this paper as the distribution of the sum of n independent but not identically distributed right truncated Poisson variables. Its p.d.f. can be expressed in terms of an R-number and an incomplete exponential function, both of which are defined and tabulated here. Properties of this R-distribution are investigated. A MVU estimate of the p.d.f. of RD is obtained. Some examples of its applications are given together with tables to facilitate the calculations.

Keywords:

• Truncated Poisson distribution
• Restricted occupancy theory
• Incomplete exponential function
• MVU estimate
• M/M/C/C queue

^∗Research supported in part by NSERC, Canada.

^∗Research supported in part by NSERC, Canada.

Notes

^∗Research supported in part by NSERC, Canada.