On the $l_p$-norm estimation of the parameters for the Jelinski-Moranda model in software reliability (CROSBI ID 176568)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Jukić, Dragan
engleski
On the $l_p$-norm estimation of the parameters for the Jelinski-Moranda model in software reliability
The exponential model of Jelinski and Moranda (1972) is one of the earliest models proposed for predicting software reliability. Estimation of its parameters has been approached in the literature by various techniques. The focus of this paper is on the $l_p$-norm $(1\leq p<\infty)$ fitting approach. Special attention is given to the nonlinear weighted least squares (LS) estimation. We show that it is possible that the best $l_p$-norm estimate does not exist. As the main result, a necessary and sufficient condition for the existence of the best $l_p$-norm estimate is obtained. This condition is theoretical in nature. We apply it to obtain two theorems on the existence of the LS estimate. One of them gives necessary and sufficient conditions which guarantee the existence of the LS estimate. To illustrate problems arising with the nonlinear normal equations approach for solving the LS problem, some illustrative examples are included.
Jelinski-Moranda model; software reliability; $l_p$-norm fitting; least squares; existence problem
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Podaci o izdanju
89 (4)
2012.
467-481
objavljeno
0020-7160
10.1080/00207160.2011.642299