Original scientific paper
Least squares fitting the three-parameter inverse Weibull density
Miljenko Marušić
orcid.org/0000-0002-7129-4670
; Department of Mathematics, University of Zagreb, Zagreb, Croatia
Darija Marković
; Department of Mathematics, University of Osijek, Osijek, Croatia
Dragan Jukić
; Department of Mathematics, University of Osijek, Osijek, Croatia
Abstract
The inverse Weibull model was developed by Erto [10].
In practice, the unknown parameters of the appropriate inverse Weibull density are not known and must be estimated from a random sample.
Estimation of its parameters has been approached
in the literature by various techniques, because a standard maximum likelihood estimate does not exist.
To estimate the unknown parameters of the three-parameter inverse
Weibull density we will use a combination of nonparametric and parametric methods.
The idea consists of using two steps: in the first step we calculate an initial nonparametric density estimate
which needs to be as good as possible, and in the second step
we apply the nonlinear least squares method to estimate the unknown parameters.
As a main result, a theorem on the existence of the least squares estimate is obtained, as well as its generalization in the $l_p$ norm ($1\leq p<\infty$).
Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.
Keywords
three-parameter inverse Weibull density; least squares; least squares estimate; existence problem; data fitting
Hrčak ID:
61878
URI
Publication date:
8.12.2010.
Visits: 3.167 *