scholarly journals Sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution

2019 ◽  
Vol 38 (28) ◽  
pp. 5413-5427 ◽  
Author(s):  
Dateng Li ◽  
Song Zhang ◽  
Jing Cao
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sample Size Calculation

scholarly journals Sampling Hazelnuts for Aflatoxin: Effect of Sample Size and Accept/Reject Limit on Reducing the Risk of Misclassifying Lots

2007 ◽  
Vol 90 (4) ◽  
pp. 1028-1035 ◽  
Author(s):  
Guner Ozay ◽  
Ferda Seyhan ◽  
Aysun Yilmaz ◽  
Thomas B Whitaker ◽  
Andrew B Slate ◽  
...  
Keyword(s):  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Food Additives ◽  
Sampling Plan ◽  
Test Results ◽  
Sampling Plans ◽  
Wide Range ◽  
Sample Test

Abstract About 100 countries have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely among regulating countries, the Codex Committee on Food Additives and Contaminants began work in 2004 to harmonize aflatoxin limits and sampling plans for aflatoxin in almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among replicated sample aflatoxin test results taken from aflatoxin-contaminated treenut lots. The uncertainty and distribution information is used to develop a model that can evaluate the performance (risk of misclassifying lots) of aflatoxin sampling plan designs for treenuts. Once the performance of aflatoxin sampling plans can be predicted, they can be designed to reduce the risks of misclassifying lots traded in either the domestic or export markets. A method was developed to evaluate the performance of sampling plans designed to detect aflatoxin in hazelnuts lots. Twenty hazelnut lots with varying levels of contamination were sampled according to an experimental protocol where 16 test samples were taken from each lot. The observed aflatoxin distribution among the 16 aflatoxin sample test results was compared to lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed distributions among sample test results taken from a wide range of lot concentrations. Using the negative binomial distribution, computer models were developed to calculate operating characteristic curves for specific aflatoxin sampling plan designs. The effect of sample size and accept/reject limits on the chances of rejecting good lots (sellers' risk) and accepting bad lots (buyers' risk) was demonstrated for various sampling plan designs.

Effects of Sample Size and Sample Acceptance Level on the Number of Aflatoxin-Contaminated Farmers’ Stock Lots Accepted and Rejected at the Buying Point

1994 ◽  
Vol 77 (6) ◽  
pp. 1672-1680 ◽  
Author(s):  
Thomas B Whitaker ◽  
Jeremy Wu ◽  
Floyd E Dowell ◽  
Winston M Hagler ◽  
Francis G Giesbrecht
Keyword(s):  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Single Sample ◽  
Sample Sizes ◽  
Acceptance Level ◽  
Aflatoxin Concentration ◽  
Acceptance Levels

Abstract Sixteen different aflatoxin sampling plan designs were evaluated using the negative-binomial distribution. Evaluations were used to predict the effects of 4 different sample sizes and 4 different sample acceptance levels on the classification of farmers’ stock lots according to the lot aflatoxin concentration. The 4 sample sizes evaluated were 2.27 kg (5 lb), 4.54 kg (10 lb), 9.08 kg (20 lb), and 18.16 kg (40 lb). The 4 sample acceptance levels evaluated were 5,50,100, and 180 ng/g. A decrease in the sample acceptance level from 180 to 5 ng/g decreased the number of lots accepted at all lot concentrations, increased the number of lots rejected at all lot concentrations, and decreased the average aflatoxin concentrations among all lots accepted. At the highest sample acceptance level, 180 ng/g, increase in sample size from 2.27 to 18.16 kg decreased the percent of lots accepted at concentrations above the sample acceptance level and increased the percent of lots accepted at concentrations below the sample acceptance level. At the lowest sample acceptance level investigated, 5 ng/g, an increase in sample size from 2.27 to 18.16 kg decreased the percent of lots accepted at all concentrations. The effect of using sampling designs with 2 sample acceptance levels to classify lots into 3 categories was investigated. The advantages of using dual sample acceptance levels over a single sample acceptance level was demonstrated for 2.27 and 9.08 kg samples.

scholarly journals Comparison of Approaches to Testing Equality of Expectations Among Samples from Poisson and Negative Binomial Distribution

2018 ◽  
Vol 66 (4) ◽  
pp. 1025-1034
Author(s):  
Martin Tejkal ◽  
Zuzana Hübnerová
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Linear Models ◽  
Negative Binomial ◽  
Test Statistics ◽  
Power Functions ◽  
Generalised Linear Models ◽  
The Relationship

The paper deals with testing of the hypothesis of equality of expectations among p samples from Poisson or negative binomial distribution. a comparison of two main approaches is carried out. The first approach is based on transforming the samples from either Poisson or negative binomial distribution in order to achieve normality or variance stability, and then testing the hypothesis of equality of expectations via the F‑test. In the second approach, test statistics coming from the theory of maximum likelihood appearing in generalised linear models framework, specially designed for testing the hypothesis among samples from the respective distributions (Poisson or negative binomial), are used. The comparison is done graphically, by plotting the simulated power functions of the test of the hypothesis of equality of expectations, when first or second approach was used. Additionally, the relationship between the power functions obtained via the respective approaches and sample sizes is studied by evaluating the respective power functions as functions of a sample size numerically.

REQUIRED SAMPLE SIZE FOR EARLY INSTAR LARVAE OF SPRUCE BUDWORM,CHORISTONEURA FUMIFERANA(LEPIDOPTERA: TORTRICIDAE), IN NEWFOUNDLAND

1983 ◽  
Vol 115 (11) ◽  
pp. 1523-1527 ◽  
Author(s):  
E. J. Dobesberger ◽  
K. P. Lim
Keyword(s):  
Population Density ◽  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Choristoneura Fumiferana ◽  
Abies Balsamea ◽  
Spruce Budworm ◽  
Balsam Fir ◽  
Early Instar

AbstractRequired sample size was determined for early instar (2nd to 4th instar) larvae of spruce budworm,Choristoneura fumiferana(Clem.). Larval counts on mid-crown 45 cm branch tips and whole branches of balsam fir,Abies balsamea(L.) Mill., were described in terms of the negative binomial distribution. The values of commonkfor the branch tip and whole branch sample units were 1.550 and 1.636, respectively. The required sample size at densities greater than or equal to one appears feasible. It is recommended that the 45 cm branch tip be used to estimate population density of early instar larvae in Newfoundland.

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.

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.

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