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On the estimation of the parameters for the Littlewood model in software reliability
Author(s) -
Barendregt L. G.,
Pul M. C.
Publication year - 1995
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1995.tb01463.x
Subject(s) - maximum likelihood , reliability (semiconductor) , software , software quality , reliability theory , process (computing) , computer science , pareto principle , estimation theory , likelihood function , mathematics , estimation , function (biology) , mathematical optimization , algorithm , statistics , software development , failure rate , power (physics) , physics , management , quantum mechanics , evolutionary biology , economics , biology , programming language , operating system
A very well‐known model in software reliability theory is that of Littlewood (1980). The (three) parameters in this model are usually estimated by means of the maximum likelihood method. The system of likelihood equations can have more than one solution. Only one of them will be consistent, however. In this paper we present a different, more analytical approach, exploiting the mathematical properties of the log‐likelihood function itself. Our belief is that the ideas and methods developed in this paper could also be of interest for statisticians working on the estimation of the parameters of the generalised Pareto distribution. For those more generally interested in maximum likelihood the paper provides a ‘practical case’, indicating how complex matters may become when only three parameters are involved. Moreover, readers not familiar with counting process theory and software reliability are given a first introduction.