Quadratic distance estimators for the zeta family

Doray, Louis G.; Luong, Andrew

doi:10.1016/0167-6687(95)00008-g

Cited by 12 publications

(12 citation statements)

References 5 publications

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“…The variance of 0 is given by V (0) = (XrZ-1X)-I. The QDE has been shown to have very high efficiency for values of p >_ l, see Doray and Luong (1995). Admittedly, there is some arbitrariness in choosing a value for k for the QDE.…”

Section: The Zeta Parametric Family and The Qdementioning

confidence: 99%

“…The zeta family is discrete and asymmetric, robustifying the MLE is not easy. (1996) [45][46][47][48][49][50][51][52][53] An alternative procedure of estimating the parameter based on quadratic distance has been developed by Doray and Luong (1995). The quadratic distance estimator (QDE) is shown in this paper to have some desirable properties, in particular the flexibility of being able to trade efficiency for robustness, see Section 2.…”

Section: ~(P + L)'mentioning

confidence: 99%

“…It allows the paper to be more self-contained. For more details concerning the QDE, we refer to Doray and Luong (1995).…”

Section: The Zeta Parametric Family and The Qdementioning

confidence: 99%

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Goodness of fit test statistics for the zeta family

Luong¹,

Doray²

1996

Insurance: Mathematics and Economics

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Goodness of fit test procedures for the zeta parametric family based on quadratic distances and the Box--Cox transform are developed. Test statistics based on quadratic distances are shown to follow a chi-square distribution asymptotically. Test procedures based on the Box-Cox transform make use of the estimator of the parameter introduced by the Box-Cox transform, and numerical computations are based on the nonlinear weighted least squares algorithms.

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Section: The Zeta Parametric Family and The Qdementioning

confidence: 99%

Section: ~(P + L)'mentioning

confidence: 99%

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Goodness of fit test statistics for the zeta family

Luong¹,

Doray²

1996

Insurance: Mathematics and Economics

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“…For more on the properties of this distribution, see Johnson et al (1992) or Doray and Luong (1995). To reflect the heterogeneity which could be present in certain populations, we will modify the basic model where all observations are identically distributed, by introducing a covariate.…”

Section: The Zeta Model With Covariatesmentioning

confidence: 99%

“…In this paper, we propose a new estimator for the regression parameters of the zeta distribution, based on the quadratic distance estimation (QDE) method used by Luong and Garrido (1993) for the (a, b) family, Doray and Luong (1995) for the zeta distribution without covariates and Doray and Luong (1997) for the Good distribution; these estimators can be obtained much more rapidly than the maximum likelihood estimators (MLEs) and possess desirable asymptotic properties.…”

Section: Introductionmentioning

confidence: 99%

Estimators of the regression parameters of the zeta distribution

Doray

Arsenault

2002

Insurance: Mathematics and Economics

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The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. We propose an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm. The quadratic distance estimator (QDE) obtained is consistent, asymptotically unbiased and normally distributed; the estimate can also serve as the initial value required by an algorithm to maximize the likelihood function. We illustrate the method with a numerical example from the insurance literature; we compare the values of the estimates obtained by the quadratic distance and maximum likelihood methods and their approximate variance-covariance matrix. Finally, we calculate the bias, variance and the asymptotic efficiency of the QDE compared to the maximum likelihood estimator (MLE) for some values of the parameters.

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Rank‐size distribution of teletraffic and customers over a wide area network

Naldi

Salaris

2006

Trans Emerging Tel Tech

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Zipf's law is used to model the uneveness of customers and telecommunications traffic distribution among the geographical areas covered by a nationwide network. Three datasets, relative to the traffic intensity in the telephone network and to the number of Internet customers as recorded on an Italian network, are used to assess the validity of the law. The estimated Zipf parameter is lower than 1 (typical of town population) in all three cases but larger than those observed for population over the same administrative groupings (code areas and provinces). Therefore the largest code areas and provinces account for a larger share of the overall traffic than what their population share would suggest, but far lower than that expected from the popularised 80/20 Pareto rule. Copyright (C) 2006 AEIT

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Quadratic distance estimators for the zeta family

Cited by 12 publications

References 5 publications

Goodness of fit test statistics for the zeta family

Goodness of fit test statistics for the zeta family

Estimators of the regression parameters of the zeta distribution

Rank‐size distribution of teletraffic and customers over a wide area network

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