Theory &amp; Methods: An EM algorithm for estimating negative binomial parameters

Adamidis, Konstantinos

doi:10.1111/1467-842x.00075

Cited by 27 publications

(11 citation statements)

References 5 publications

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“…As pointed out by Little and Rubin (1983), the EM algorithm converge reliably but rather slowly, compared with the Newton-Raphson method, when the amount of information in the missing data is relatively large. Recently, EM algorithm has been used by such researchers as Adamidis and Loukas (1998), Adamidis (1999), Ng et al (2002), Karlis (2003), and Adamidis et al (2005).…”

Section: Em Algorithmmentioning

confidence: 99%

Generalized extended Weibull power series family of distributions

Alkarni¹

2021

Journal of Data Science

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In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.

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Section: Em Algorithmmentioning

confidence: 99%

Generalized extended Weibull power series family of distributions

Alkarni¹

2021

Journal of Data Science

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“…The NBRM was explored in Adamidis (1999); Greene (2008); Lawless (1987aLawless ( , 1987b, and Raschke and Greene (2010); Hilbe (2011) and Hilbe (2014) provide useful recent surveys of the NBRM. 10 Common variants of this argument include: (i) Lee (1986), who specifies the gamma distribution in terms of the shape and scale (or inverse rate) (ξ = 1/η) parameters, that is, θ ∼ G(1/ξ, τ), and (ii) Cameron and Trivedi (1986), who use the so-called index form of the gamma distribution, which is specified in terms of the shape and mean (φ = τ/η) parameters, that is, θ ∼ G(τ/φ, τ).…”

Section: The Classical Negative Binomial Regression Modelmentioning

confidence: 99%

Distributions You Can Count On …But What’s the Point?

McCabe

Skeels

2020

Econometrics

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The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.

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“…The main drawback of the EM algorithm is its rather slow convergence, compared to the Newton-Raphson method, when the "missing data" contain relatively large amount of information (Little and Rubin, 1983). Recently, several researchers have used the EM method such as Adamidis et al (2005), Karlis (2003), Ng et al (2002), Adamidis and Loukas (1998), Adamidis (1999), among others. Newton-Raphson is required for the M-step of the EM algorithm.…”

Section: Estimationmentioning

confidence: 99%

The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

Rahmouni

Orabi

2017

IJSP

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This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

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Theory & Methods: An EM algorithm for estimating negative binomial parameters

Cited by 27 publications

References 5 publications

Generalized extended Weibull power series family of distributions

Generalized extended Weibull power series family of distributions

Distributions You Can Count On …But What’s the Point?

The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

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