Naslov
On the $l_p$-norm estimation of the parameters for the Jelinski-Moranda model in software reliability

Autori
Jukić, Dragan

Izvornik
International journal of computer mathematics (0020-7160) 89 (2012), 4; 467-481

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jelinski-Moranda model; software reliability; $l_p$-norm fitting; least squares; existence problem

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo

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