On nonlinear weighted least squares fitting of the three-parameter inverse Weibull distribution (CROSBI ID 150117)
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Jukić, Dragan ; Marković, Darija
engleski
On nonlinear weighted least squares fitting of the three-parameter inverse Weibull distribution
In this paper we consider nonlinear least squares fitting of the three-parameter inverse Weibull distribution to the given data $(w_i, t_i, y_i)$, $i=1, \ldots, n$, $n\geq 3$. As the main result, we show that the least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) $0<t_1<t_2<\ldots<t_n$ and (ii) $0<y_1<y_2<\ldots<y_n<1$. To this end, an illustrative numerical example is given.
three-parameter inverse Weibull distribution; data fitting; nonlinear least squares; least squares estimate; existence problem
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