A new generalization of the Waring distribution

Avi, José Rodríguez; Sánchez, Antonio Conde; Sáez-Castillo, A. J.; Olmo-Jiménez, María José

doi:10.1016/j.csda.2006.12.029

Cited by 21 publications

(24 citation statements)

References 21 publications

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“…For example, methods based on Waring distributions and regression (e.g. Irwin, 1968; Xekalaki, 1983, 1984; Rodríguez‐Avi et al, 2007, 2009) use parametric distributions based on Poisson, Gamma and Beta distributions to decompose variation into several components: randomness and between‐subject heterogeneity explainable by covariates (liability) or intrinsic to individuals (proneness). Our models could be viewed in terms of decompositions using random effects, into components between subjects described by u i and any subject‐level covariates (e.g.…”

Section: Discussionmentioning

confidence: 99%

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A statistical model for under- or overdispersed clustered and longitudinal count data

et al. 2011

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We propose a likelihood-based model for correlated count data that display under- or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth-event processes is used to model within-subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.

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Section: Discussionmentioning

confidence: 99%

“…This approach has been extended to further decompose components of variation in count data using generalized Waring distributions and Waring regression (e.g. Irwin, 1968; Xekalaki, 1983, 1984; Rodríguez‐Avi et al, 2007, 2009), and also to allow different forms of covariate effects in Negative Binomial models (e.g. Greene, 2007).…”

Section: Introductionmentioning

confidence: 99%

A statistical model for under- or overdispersed clustered and longitudinal count data

et al. 2011

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“…Specifically, according to the classification this is given in Rodríguez-Avi et al (2007), it is a GHD of type VII, but it had not been studied in particular. Thus, some of the properties that are shown in the paper were not known, mainly its origin as a binomial mixture like the beta-binomial distribution, which may be considered as a particular case of the GBB distribution with λ = 1: We observe that the beta-binomial distribution does not belong to the PSD class.…”

Section: Authors' Responsementioning

confidence: 99%

“…A generalization of the beta-binomial distribution Rodríguez-Avi et al (2007) proposed a generalization of the beta-binomial distribution with some applications. The new distribution of the paper was defined by the probability mass function:…”

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Authors’ Response

Avi¹,

Sánchez²,

Sáez-Castillo³

et al. 2007

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Sarabia & Castillo (2003) proposed two multivariate extensions of this distribution: one by means of the Sarmanov-Lee distribution with beta marginal, and the other using the concept of the conditional specification of distributions. Finally, Rodríguez-Avi et al (2003) studied different parameter estimation methods based on moments and/ or frequencies for Gauss' family of hypergeometric distributions, while they (Rodríguez-Avi et al, 2007) presented an example with which they compared the results obtained applying the maximum likelihood method to the negative binomial distribution, the univariate generalized Waring distribution and the extended Waring distribution, the latter being a tetraparametric univariate distribution generated by Gauss' hypergeometric function. This includes the generalized Waring distribution, as a combination of the negative binomial distribution and the beta type 1 generalized distribution.…”

Section: Waring Distributionmentioning

confidence: 99%

Modelling the number of olive groves in Spanish municipalities

Huete

Marmolejo

2016

Span. j. agric. res.

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The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives p-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.Additional key words: table olive; oil olive; agricultural holdings; Waring distribution; estimation. Abbreviations used: L (liability); MF12 (method of one equation of moments and two relations between frequency); MF21 (method of two relations between moments and one equation of frequency); MLE (method of log-likelihood optimisation); MM3 (method of the three relations between moments); P (proneness); R (randomness); UGWD (Univariate Generalized Waring Distribution).

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A new generalization of the Waring distribution

Cited by 21 publications

References 21 publications

A statistical model for under- or overdispersed clustered and longitudinal count data

A statistical model for under- or overdispersed clustered and longitudinal count data

Authors’ Response

Modelling the number of olive groves in Spanish municipalities

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