A General Solution of the Integral Equation for Erlang Distribution

- Journal title : Communications for Statistical Applications and Methods
- Volume 12, Issue 2, 2005, pp.435-442
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2005.12.2.435

Title & Authors

A General Solution of the Integral Equation for Erlang Distribution

Lee Yoon Dong; Choi Hyemi; Lee Eun-kyung;

Lee Yoon Dong; Choi Hyemi; Lee Eun-kyung;

Abstract

The mathematical properties of the sequentially operated systems are often described by integral equations. Reservoir system of a product and sequential probability ratio test (SPRT) are typical examples of sequentially operated systems. When the underlying random quantities follow Erlang distribution, a systematic method was developed to solve the integral equations. We extend the method to the cases having accrual functions of more general types. The solutions of the integral equations are represented as a linear combination of distribution functions, and the coefficients of the linear combination are obtained by solving linear system derived from the continuity condition of the solutions.

Keywords

Erlang distribution;SPRT;Integral equation;

Language

English

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