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

Jukić, Dragan; Benšić, Mirta; Scitovski, Rudolf

doi:10.1016/j.csda.2008.03.001

Cited by 32 publications

(19 citation statements)

References 7 publications

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“…In general, the inertia weight ω has a linearly decreasing dynamic parameter framework descending from ω max to ω min as shown in Eq. (8). According to Das et al [46], for inertia weight, ω max to ω min are 0.9 and 0.4, respectively produces satisfactory results.…”

Section: Implementation Of Pso To 3-p Weibull Parameter Estimation Anmentioning

confidence: 69%

“…Iter max Iter (8) where ω max and ω min are the initial and final inertia weights, Iter max is maximum iteration number and Iter is current iteration number [43]. Usually, parameters ω max and ω min are set to 0.9 and 0.4, respectively.…”

Section: Particle Swarm Optimizationmentioning

confidence: 99%

“…Cousineau [5] reviewed estimation methods for three-parameter Weibull distribution. Bartolucci et al [6], Bartkute and Sakalauskas [7], Jukic et al [8], Markovich et al [9] Jukic and Markovich [10], and Markovich and Jukic [11] examined moments method for Weibull distribution. The most common way of estimating the parameters of the density function from the observed data is the maximum likelihood method for Weibull distribution [12][13][14][15].…”

Section: Literature Surveymentioning

confidence: 99%

See 2 more Smart Citations

Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

Örkçü

Özsoy

Aksoy

et al. 2015

Applied Mathematics and Computation

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Section: Implementation Of Pso To 3-p Weibull Parameter Estimation Anmentioning

confidence: 69%

Section: Particle Swarm Optimizationmentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

See 1 more Smart Citation

Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

Örkçü

Özsoy

Aksoy

et al. 2015

Applied Mathematics and Computation

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“…The problem of nonlinear weighted LS and total least squares fitting of the Bass curve (2) is considered by Jukić (2013;2011). Results on the existence of the LS estimate for some other special classes of functions can be found in the works of Bates and Watts (1988), Björck (1996), Demidenko (2008;2006;, Hadeler et al (2007), Jukić (2013;2009), Jukić and, Jukić et al (2008;, Marković and Jukić (2010), as well as Marković et al (2009).…”

Section: Introductionmentioning

confidence: 98%

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Marković¹,

Jukić²

2013

International Journal of Applied Mathematics and Computer Science

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The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.

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“…However, for the three-parameter Weibull distribution the likelihood function is unbounded from above so that a standard ML estimate does not exist (see e.g. [11,15]). Some of the existing results regarding parameter estimation of the three-parameter Weibull distribution are based on finding a local maximum of the likelihood function, if it exists.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start

Marković

Jukić

Benšić

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density estimate which needs to be as good as possible, and then 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. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.

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

Cited by 32 publications

References 7 publications

Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start

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