A Series Approximation for Negative Binomial Parameter Estimation

1969 ◽  
Vol 6 (3) ◽  
pp. 355-356 ◽  
Author(s):  
Donald G. Morrison
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial Distribution ◽  
Negative Binomial ◽  
Search Procedure ◽  
Iterative Search ◽  
Implicit Equation ◽  
Series Approximation ◽  
Binomial Parameter ◽  
Nbd Model ◽  
Parameter Values

One parameter of the negative binomial distribution (NBD) model of repeat purchase loyalty is obtained by an iterative search procedure on an implicit equation. This note presents an extremely accurate explicit series approximation for this parameter. When solving for the parameters by hand, one can use some very efficient table to look up procedures. However, when a researcher is solving for many sets of parameter values, our procedure is much easier to program.

scholarly journals Suitability of Several Statistical Models to Simulate Observed Distribution of Sample Test Results in Inspections of Aflatoxin-Contaminated Peanut Lots

1996 ◽  
Vol 79 (4) ◽  
pp. 981-988 ◽  
Author(s):  
Thomas Whitaker ◽  
Francis Giesbrecht ◽  
Jeremy Wu
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Statistical Models ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Results ◽  
Parameter Estimation Method

Abstract The acceptability of 10 theoretical distributions to simulate observed distribution of sample aflatoxin test results was evaluated by using 2 parameter estimation methods and 3 goodness of fit (GOF) tests. All theoretical distributions were compared with 120 observed distributions of aflatoxin test results of farmers' stock peanuts. For a given parameter estimation method and GOF test, the negative binomial distribution had the highest percentage of statistically acceptable fits. The log normal and Poisson-gamma (gamma shape parameter = 0.5) distributions had slightly fewer but an almost equal percentage of acceptable fits. For the 3 most acceptable statistical models, the negative binomial had the greatest percentage of best or closest fits. Both the parameter estimation method and the GOF test had an influence on which theoretical distribution had the largest number of acceptable fits. All theoretical distributions, except the negative binomial distribution, had more acceptable fits when model parameters were determined by the maximum likelihood method. The negative binomial had slightly more acceptable fits when model parameters were estimated by the method of moments. The results also demonstrated the importance of using the same GOF test for comparing the acceptability of several theoretical distributions.

The Development of Topic Model Based on Beta-Negative Binomial Process

2013 ◽  
Vol 427-429 ◽  
pp. 1597-1600
Author(s):  
Ya Shu Liu ◽  
Han Bing Yan
Keyword(s):  
Data Mining ◽  
Parameter Estimation ◽  
Gibbs Sampling ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Topic Model ◽  
Negative Binomial Process ◽  
Binomial Process ◽  
Design Experiments

. Topic Model is one of the important subfields in Data Mining, which has been developed very quickly and has been applicated in many fields in recent years. Many researchers have been engaged in this field. In this paper, we introduce the BNB process based on Beta and Negative Binomial distribution, using the hierarchical distribution instead of Dirichlet in LDA. And we give the expression of parameter estimation used by Gibbs sampling. Then, BNB process is applicated in the text topic classification. We design experiments to decide the numbers of topics and compare the BNB process with LDA. Experiment results show that the BNB process has better performance over LDA in English Dataset, but they have almost the same result in Chinese micro-blog topic classification. Finally we analyze the problem and give the idea in further research.

Conditional Trend Analysis: A Model that Allows for Nonusers

1969 ◽  
Vol 6 (3) ◽  
pp. 342-346 ◽  
Author(s):  
Donald G. Morrison
Keyword(s):  
Simple Model ◽  
Stochastic Model ◽  
Trend Analysis ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Product Category ◽  
Systematic Bias ◽  
Explicit Formulas ◽  
Nbd Model

Goodhardt and Ehrenberg have developed a useful stochastic model for analyzing period-to-period fluctuations in sales. In this article we generalize their model to allow for nonbuyers of the product category. A systematic bias in their simple negative binomial distribution (NBD) model is demonstrated. In fact if the proportion of nonbuyers is large, the simple model will be wrong. We also give explicit formulas and directions that allow a moderately sophisticated analyst to perform his own conditional trend analysis.

scholarly journals Can the negative binomial distribution predict industrial purchases?

2016 ◽  
Vol 31 (4) ◽  
pp. 543-552 ◽  
Author(s):  
John W. Wilkinson ◽  
Giang Trinh ◽  
Richard Lee ◽  
Neil Brown
Keyword(s):  
Boundary Conditions ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Data Set ◽  
Content Type ◽  
Significant Difference ◽  
Industrial Purchasing ◽  
Nbd Model ◽  
Purchasing Patterns

Purpose This paper aims to extend the known boundary conditions of the negative binomial distribution (NBD) model, and to test the applicability of conditional trend analysis (CTA) – a key method to identify whether changes in overall sales are accounted for by previous non-buyers, light buyers or heavy buyers – in industrial purchasing situations. Design/methodology/approach The study tested the NBD model and CTA in an industrial marketing context using a 12-month data set of purchases from an Australian supplier of a range of industrial plastic resins. Findings The purchase data displayed a good NBD fit; the study therefore extends the known boundary conditions of the model. The application of CTA provided second-period purchasing frequency estimates showing no significant difference from actual data, indicating the applicability of this method to industrial purchasing. Research limitations/implications Data relate to just one supplier. Further research across several industries is required to confirm the generalizability and robustness of NBD and CTA to industrial markets. Practical implications Marketing decisions can be improved through appropriate analysis of customer purchasing data. However, without access to equivalent competitor data, industrial marketers are constrained in benchmarking the purchasing patterns of their own customers. The results indicate that use of the NBD model enables valid benchmarking for industrial products, while CTA would enable appropriate analysis of purchases by different classes of customer. Originality/value This paper extends the known boundary conditions of the NBD model and provides the first published results, indicating the appropriateness of CTA to predict purchasing frequencies of different industrial customer classes.

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

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.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

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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