engleski

On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution

The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data$(w_i, t_i, y_i)$, $i=1, \ldots, n$, is considererd. The part $w_i>0$ of the data stands for the data weights. It is shown that the best least squares estimate exists, provided that the data satisfy only 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 support this, an illustrative numerical example is given.

three-parameter Weibull distribution; data fitting; nonlinear least squares; least squares estimate; existence problem

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