scholarly journals On hypergeometric generalized negative binomial distribution

2002 ◽  
Vol 29 (12) ◽  
pp. 727-736 ◽  
Author(s):  
M. E. Ghitany ◽  
S. A. Al-Awadhi ◽  
S. L. Kalla
Keyword(s):  
Recurrence Relation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
The Right ◽  
Three Term Recurrence Relation

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

Patterns of macroparasite aggregation in wildlife host populations

Parasitology ◽  
1998 ◽  
Vol 117 (6) ◽  
pp. 597-610 ◽  
Author(s):  
D. J. SHAW ◽  
B. T. GRENFELL ◽  
A. P. DOBSON
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Data Sets ◽  
Frequency Distributions ◽  
System A ◽  
Host Sex ◽  
Host Parasite

Frequency distributions from 49 published wildlife host–macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host–parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

scholarly journals DISTRIBUCIÓN ESPACIAL DE Vatiga spp. (HEMIPTERA: TINGIDAE) EN EL CULTIVO DE YUCA

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Antonio De Souza Silva
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Negative Binomial ◽  
Plant Leaves ◽  
Frequency Distributions ◽  
Morisita Index ◽  
Best Fit

<p class="p1"> <strong>RESUMEN</strong></p><p class="p3">El objetivo de este trabajo fue generar informacion acerca de cuál es el modelo de disposición espacial de Vatiga spp. en el cultivo de la yuca. Se realizaron muestreos en dos áreas comerciales de 2500 m<span class="s1">2</span>, divididas en 100 parcelas. Se contaron adultos y de ninfas de Vatiga spp. en las hojas basales y medias de la planta. En total, se realizaron doce muestreos quincenalmente, desde febrero hasta abril de 2014, época de mayor incidencia de esta plaga. De forma general, a través de los índices de dispersión (varianza/media, índice de Morisita y exponente K) y las distribuciones de frecuencia, se observa que la distribución espacial de Vatiga spp. es agregada, es decir, el padrón de distribución Binomial Negativa fue el que resultó de mejor ajuste a los datos obtenidos a campo, con el conteo de los individuos.</p><p class="p1"><strong>ABSTRACT</strong></p><p class="p2">The aim of this study was to generate information about which is the model of spatial distribution of Vatiga spp. in the cassava culture. Sampling was conducted in two commercial areas of 2,500 m<span class="s1">2</span>, divided into 100 plots. Adults and nymphs of Vatiga spp. were counted in the basal and medium plant leaves. In all, twelve samples were taken fortnightly from February to April 2014, when occurs the highest incidence of this pest. Based in the indices of dispersion (variance/mean, Morisita index and K exponent) and the frequency distributions, it was observed that the spatial distribution of Vatiga spp. is aggregate, it means that the standard Negative Binomial distribution was the best fit to the field data obtained, with the counting direction of individuals.</p>

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