Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution

2013 ◽  
Vol 83 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Hongsheng Dai ◽  
Yanchun Bao ◽  
Mingtang Bao
Keyword(s):  
Maximum Likelihood ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Maximum Likelihood Estimate ◽  
Negative Binomial ◽  
Likelihood Estimate ◽  
Dispersion Parameter

Adjustment for Maximum Likelihood Estimate of Negative Binomial Dispersion Parameter

2008 ◽  
Vol 2061 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Byung-Jung Park ◽  
Dominique Lord
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimate ◽  
Negative Binomial ◽  
Highway Safety ◽  
Likelihood Estimate ◽  
Dispersion Parameter ◽  
Dispersion Parameters ◽  
Sample Mean ◽  
Crash Data

The negative binomial (NB) (or Poisson–gamma) model has been used extensively by highway safety analysts because it can accommodate the overdispersion often exhibited in crash data. However, it has been reported in the literature that the maximum likelihood estimate of the dispersion parameter of NB models can be significantly affected when the data are characterized by small sample size and low sample mean. Given the important roles of the dispersion parameter in various types of highway safety analyses, there is a need to determine whether the bias could be potentially corrected or minimized. The objectives of this study are to explore whether a systematic relationship exists between the estimated and true dispersion parameters, determine the bias as a function of the sample size and sample mean, and develop a procedure for correcting the bias caused by these two conditions. For this purpose, simulated data were used to derive the relationship under the various combinations of sample mean, dispersion parameter, and sample size, which encompass all simulation conditions performed in previous research. The dispersion parameter was estimated by using the maximum likelihood method. The results confirmed previous studies and developed a reasonable relationship between the estimated and true dispersion parameters for reducing the bias. Details for the application of the correction procedure were also provided by using the crash data collected at 458 three-leg unsignalized intersections in California. Finally, the study provided several discussion points for further work.

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.

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (4) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (04) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn ; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p 0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p 0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Sign in / Sign up

Export Citation Format

Share Document