Ehrenberg's Negative Binomial Model Applied to Grocery Store Trips

1980 ◽  
Vol 17 (3) ◽  
pp. 385-390 ◽  
Author(s):  
Gil A. Frisbie
Keyword(s):  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Grocery Store ◽  
Distribution Model ◽  
Grocery Stores ◽  
Good Representation ◽  
Binomial Model ◽  
Food Stores ◽  
Goodness Of Fit Tests

Ehrenberg's negative binomial distribution model is applied to a new facet of consumer behavior, the frequency of household filler trips to food stores. Goodness-of-fit tests and intertemporal predictions are assessed. The overall verdict is that the model serves as a good representation of the trips to grocery stores.

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.

The Stability of Weed Seedling Population Models and Parameters in Eastern Nebraska Corn (Zea mays) and Soybean (Glycine max) Fields

Weed Science ◽  
1995 ◽  
Vol 43 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Distribution Model ◽  
Ratio Test ◽  
Weed Species ◽  
Sampling Procedures ◽  
Grass Weed

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.

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

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.

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 Best Fitted Distribution For Meteorological Data In Kuala Krai

2021 ◽  
Vol 3 (1) ◽  
pp. 16-25
Author(s):  
Siti Mariam Norrulashikin ◽  
Fadhilah Yusof ◽  
Siti Rohani Mohd Nor ◽  
Nur Arina Bazilah Kamisan
Keyword(s):  
Climate Change ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Meteorological Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

scholarly journals Modeling Traffic Accident Occurrence at Hazardous Road Locations: A Case Study in Tunisia

2018 ◽  
Author(s):  
Fedy Ouni ◽  
Mounir Belloumi
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Prediction Models ◽  
Pearson Correlation ◽  
Surface Condition ◽  
Random Effect ◽  
Negative Binomial Model ◽  
Empirical Modeling ◽  
Binomial Model ◽  
Model Average

The purpose of the present study is to explore the linkage between Hazardous Road Locations-based crash counts and a variety of geometric characteristics, roadway characteristics, traffic flow characteristics and spatial features in the region of Sousse, Tunisia. For this purpose, collision data was collected from at 52 hazardous road sections including 1397 crash records for a 11-year monitoring period from January 1, 2004 to December 31, 2014 obtained from National Observatory for Information, Training, Documentation and Studies on Road Safety in Tunisia (NOITDRS). The matrix of Pearson correlation was used in order to avoid inclusion of both variables, which were highly correlated. Both the Random Effects Negative Binomial model and the Negative Binomial model were estimated. To evaluate the models, the Random Effect Negative Binomial model improves the goodness-of-fit compared to the Negative Binomial model. Average Daily Traffic volume, Curved alignment, Presence of public lighting, Visibility, Number of lane, Presence of vertical/horizontal sign, Presence of rural segment, Presence of drainage system, Roadway surface condition, Presence of paved shoulder and presence of major road were found as significant variables influencing accident occurrences. Overall, the current research contributes to the literature from empirical, modeling methodological standpoints since it was the first study conducted in Tunisia to use crash prediction models for hazardous road locations, and that portrays Tunisian reality. The research findings present advantageous insights on hazardous road locations in the region of Sousse, Tunisia and present useful planning tools for public authorities in Tunisia.

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