Correction to: Measured PET Data Characterization with the Negative Binomial Distribution Model

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is akparameter.kis a nonspatial aggregation parameter related to the variance at a given mean value. Thekparameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of thekparameter across field sites was assessed using the likelihood ratio test There was no stable or commonkvalue across field sites and years for all weed species populations. The lack of stability inkacross field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Becausekis not stable across field sites,kmust be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

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Spatial Distribution of Eggs of Alabama argillacea Hübner and Heliothis virescens Fabricius (Lepidoptera: Noctuidae) on Bt and non-BtCotton

Anais da Academia Brasileira de Ciências ◽

10.1590/0001-3765201520140297 ◽

2015 ◽

Vol 87 (4) ◽

pp. 2243-2253

Author(s):

TATIANA R. RODRIGUES ◽

MARCOS G. FERNANDES ◽

PAULO E. DEGRANDE ◽

THIAGO A. MOTA

Keyword(s):

Spatial Distribution ◽

Negative Binomial Distribution ◽

Binomial Distribution ◽

Heliothis Virescens ◽

Negative Binomial ◽

Model Fitting ◽

Spatial Arrangement ◽

Distribution Model ◽

Aggregation Index ◽

Alabama Argillacea

ABSTRACT Among the options to control Alabama argillacea (Hübner, 1818) and Heliothis virescens (Fabricius, 1781) on cotton, insecticide spraying and biological control have been extensively used. The GM'Bt' cotton has been introduced as an extremely viable alternative, but it is yet not known how transgenic plants affect populations of organisms that are interrelated in an agroecosystem. For this reason, it is important to know how the spatial arrangement of pests and beneficial insect are affected, which may call for changes in the methods used for sampling these species. This study was conducted with the goal to investigate the pattern of spatial distribution of eggs of A. argillacea and H. virescens in DeltaOpalTM (non-Bt) and DP90BTMBt cotton cultivars. Data were collected during the agricultural year 2006/2007 in two areas of 5,000 m2, located in in the district of Nova América, Caarapó municipality. In each sampling area, comprising 100 plots of 50 m2, 15 evaluations were performed on two plants per plot. The sampling consisted in counting the eggs. The aggregation index (variance/mean ratio, Morisita index and exponent k of the negative binomial distribution) and chi-square fit of the observed and expected values to the theoretical frequency distribution (Poisson, Binomial and Negative Binomial Positive), showed that in both cultivars, the eggs of these species are distributed according to the aggregate distribution model, fitting the pattern of negative binomial distribution.

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Measured PET Data Characterization with the Negative Binomial Distribution Model

Journal of Medical and Biological Engineering ◽

10.1007/s40846-017-0236-2 ◽

2017 ◽

Vol 37 (3) ◽

pp. 299-312 ◽

Cited By ~ 3

Author(s):

Maria Filomena Santarelli ◽

Vincenzo Positano ◽

Luigi Landini

Keyword(s):

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Distribution Model

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Use of a negative binomial distribution to describe the presence of Sphyrion laevigatum in Genypterus blacodes

Revista Brasileira de Parasitologia Veterinária ◽

10.1590/s1984-29612013000400024 ◽

2013 ◽

Vol 22 (4) ◽

pp. 602-604 ◽

Cited By ~ 2

Author(s):

Patricio Peña-Rehbein ◽

Patricio De los Ríos-Escalante ◽

Raúl Castro ◽

Carolina Navarrete

Keyword(s):

Spatial Distribution ◽

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Distribution Model ◽

Economic Resource ◽

Spatial Distribution Model

This paper describes the frequency and number of Sphyrion laevigatum in the skin of Genypterus blacodes, an important economic resource in Chile. The analysis of a spatial distribution model indicated that the parasites tended to cluster. Variations in the number of parasites per host could be described by a negative binomial distribution. The maximum number of parasites observed per host was two.

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Testing the odds of inherent vs. observed overdispersion in neural spike counts

Journal of Neurophysiology ◽

10.1152/jn.00194.2015 ◽

2016 ◽

Vol 115 (1) ◽

pp. 434-444 ◽

Cited By ~ 5

Author(s):

Wahiba Taouali ◽

Giacomo Benvenuti ◽

Pascal Wallisch ◽

Frédéric Chavane ◽

Laurent U. Perrinet

Keyword(s):

Poisson Process ◽

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Poisson Model ◽

Probabilistic Methods ◽

Distribution Model ◽

Data Sets ◽

Electrophysiological Recordings ◽

Neurophysiological Data

The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within the neural activity. In that case, a Poisson process is the most common model of trial-to-trial variability. For a Poisson process, the variance of the spike count is constrained to be equal to the mean, irrespective of the duration of measurements. Numerous studies have shown that this relationship does not generally hold. Specifically, a majority of electrophysiological recordings show an “overdispersion” effect: responses that exhibit more intertrial variability than expected from a Poisson process alone. A model that is particularly well suited to quantify overdispersion is the Negative-Binomial distribution model. This model is well-studied and widely used but has only recently been applied to neuroscience. In this article, we address three main issues. First, we describe how the Negative-Binomial distribution provides a model apt to account for overdispersed spike counts. Second, we quantify the significance of this model for any neurophysiological data by proposing a statistical test, which quantifies the odds that overdispersion could be due to the limited number of repetitions (trials). We apply this test to three neurophysiological data sets along the visual pathway. Finally, we compare the performance of this model to the Poisson model on a population decoding task. We show that the decoding accuracy is improved when accounting for overdispersion, especially under the hypothesis of tuned overdispersion.

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Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

Vestnik Zoologii ◽

10.2478/vzoo-2019-0037 ◽

2019 ◽

Vol 53 (5) ◽

pp. 417-422

Author(s):

P. De los Ríos ◽

E. Ibáñez Arancibia

Keyword(s):

Spatial Distribution ◽

Negative Binomial Distribution ◽

Binomial Distribution ◽

Rocky Shore ◽

Negative Binomial ◽

Null Model ◽

Easter Island ◽

Published Data ◽

Distribution Analysis ◽

Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

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ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

Journal of Mathematics and Its Applications ◽

10.29244/jmap.10.2.1-10 ◽

2011 ◽

Vol 10 (2) ◽

pp. 1

Author(s):

Y. ARBI ◽

R. BUDIARTI ◽

I G. P. PURNABA

Keyword(s):

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Financial Institution ◽

Expected Value ◽

Insurance Companies ◽

Limited Data ◽

Loss Distribution Approach ◽

Potential Loss ◽

The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

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

Mathematics ◽

10.3390/math9131571 ◽

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.

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