Fitting a Negative Binomial Distribution to Coarsely Grouped Data by Maximum Likelihood

1962 ◽  
Vol 11 (3) ◽  
pp. 196 ◽  
Author(s):  
F. M. O'Carroll
Keyword(s):  
Maximum Likelihood ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Grouped Data

scholarly journals A Bivariate Model based on Compound Negative Binomial Distribution

2018 ◽  
Vol 41 (1) ◽  
pp. 87-108 ◽  
Author(s):  
Maha Ahmad Omair ◽  
Fatimah E AlMuhayfith ◽  
Abdulhamid A Alzaid
Keyword(s):  
Maximum Likelihood ◽  
Method Of Moments ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Traffic Accidents ◽  
Negative Binomial ◽  
Conditional Distributions ◽  
Bivariate Model ◽  
Distributional Properties ◽  
Parameter Estimators

A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.

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.

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