The Poisson Pascal Distribution

Katti, S. K.; Gurland, John

doi:10.2307/2527853

Cited by 44 publications

(20 citation statements)

References 7 publications

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“…The results obtained by the method of moments show that the distribution is virtually biparametric, as the value of k is practically zero in most cases. Rodríguez-Avi et al (2003) obtained a value of k < 0.067 using the data reported by Beal & Rescia (1953) and by Katti & Gurland (1961). Canal & Micciolo (1999) also obtained values of 0.476 and 0.720 in the fits obtained k for patients' psychiatric records.…”

Section: Discussionmentioning

confidence: 70%

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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Section: Discussionmentioning

confidence: 70%

Modelling the number of olive groves in Spanish municipalities

Huete

Marmolejo

2016

Span. j. agric. res.

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“…Gurland It is also evident from Table I that appear in a number of recent papers. Gurland (1960), (1961), Katti and Gurland (1961), ( The Negative Binomial is one of the most widely used discrete distributions because it is relatively simple and is very convenient computationally although the estimation of the parameters is rather tedious if the method of maximum likelihood is employed (cf. Fisher(1953) Bliss (1953).…”

Section: Say (Q -Plz)mentioning

confidence: 99%

“…Estimation of the parameters in this distribution by the technique of minimum chi-square is considered by Katti and Gurland (1961). In Table 3, taken from this paper, we see the results of fitting a Poisson v Pascal and a Polya-Aeppli to some data of Beall and Rescia (1953).…”

Section: Say (Q -Plz)mentioning

confidence: 99%

Some Families of Compound and Generalized Distributions

Gurland¹

1963

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“…, one obtains the Pólya-Aeppli models that are useful for zero-heavy data and can be posed as the Poisson stopped sum of the negative binomial model (Katti and Gurland, 1961). The limit of (2) when β tends to 0, p tends to 2, is…”

Section: Introductionmentioning

confidence: 99%

Extended Truncated Tweedie-Poisson Model

Valero¹,

Ginebra

Pérez-Casany

2012

Methodol Comput Appl Probab

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Abstract. It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed Poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

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The Poisson Pascal Distribution

Cited by 44 publications

References 7 publications

Modelling the number of olive groves in Spanish municipalities

Modelling the number of olive groves in Spanish municipalities

Some Families of Compound and Generalized Distributions

Extended Truncated Tweedie-Poisson Model

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