An Approximate Pitman-Type “Close” Estimator for the Negative Binomial Parameter p

Technometrics ◽  
1972 ◽  
Vol 14 (1) ◽  
pp. 77-88 ◽  
Author(s):  
J. M. Maynard ◽  
B. Chow
1970 ◽  
Vol 102 (10) ◽  
pp. 1216-1222 ◽  
Author(s):  
M. K. Mukerji ◽  
D. G. Harcourt

AbstractCounts of the cabbage maggot, Hylemya brassicae (Bouché), on cabbage did not conform to the Poisson distribution, there being an excess of uninfested and highly infested plants over the expected number. But when the negative binomial series was fitted to the observed distribution, the discrepancies were not significant when tested by chi-square. The negative binomial parameter k tended to increase with density. Using a common k, the distribution of the various stages may be described by expansion of (q − p)−k, when values of k are as follows: egg 0.78, larva 0.71, pupa 0.84. Three different transformations are offered for stabilizing the variance of field counts.


Parasitology ◽  
2019 ◽  
Vol 147 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Richard C. Tinsley ◽  
Hanna Rose Vineer ◽  
Rebecca Grainger-Wood ◽  
Eric R. Morgan

AbstractThe almost universally-occurring aggregated distributions of helminth burdens in host populations have major significance for parasite population ecology and evolutionary biology, but the mechanisms generating heterogeneity remain poorly understood. For the direct life cycle monogenean Discocotyle sagittata infecting rainbow trout, Oncorhynchus mykiss, variables potentially influencing aggregation can be analysed individually. This study was based at a fish farm where every host individual becomes infected by D. sagittata during each annual transmission period. Worm burdens were examined in one trout population maintained in isolation for 9 years, exposed to self-contained transmission. After this year-on-year recruitment, prevalence was 100% with intensities 10–2628, mean 576, worms per host. Parasite distribution, amongst hosts with the same age and environmental experience, was highly aggregated with variance to mean ratio 834 and negative binomial parameter, k, 0.64. The most heavily infected 20% of fish carried around 80% of the total adult parasite population. Aggregation develops within the first weeks post-infection; hosts typically carried intensities of successive age-specific cohorts that were consistent for that individual, such that heavily-infected individuals carried high numbers of all parasite age classes. Results suggest that host factors alone, operating post-infection, are sufficient to generate strongly overdispersed parasite distributions, rather than heterogeneity in exposure and initial invasion.


1969 ◽  
Vol 6 (3) ◽  
pp. 355-356 ◽  
Author(s):  
Donald G. Morrison

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.


1963 ◽  
Vol 95 (8) ◽  
pp. 813-820 ◽  
Author(s):  
D. G. Harcourt

AbstractCounts of the Colorado potato beetle on potato did not conform to the Poisson distribution, there being an excess of uninfested and highly infested hills over the expected numbers. However, when observed distributions were fitted to the negative binomial series, the discrepancies were not significant when tested by chi-square. The negative binomial parameterktended to increase with density. Using a commonk, the distribution of the various stages may be described by expansion of (q−px)−k, when values ofkare as follows: adult, 1.95; egg mass, 4.10; first instar, 0.68; second instar, 0.78; third instar, 1.04; fourth instar, 1.07.For all stages, the variance was proportional to a fractional power of the mean. Use of the individual potato stalk as a sample unit had little effect on the skewness of the distribution. Four transformations are offered for stabilizing the variance of field counts.


Biometrics ◽  
1989 ◽  
Vol 45 (1) ◽  
pp. 309 ◽  
Author(s):  
Suzanne J. Clark ◽  
Joe N. Perry

2016 ◽  
Vol 11 (3) ◽  
pp. 55-66
Author(s):  
Maury Granger ◽  
Gregory Price

AbstractIf alcohol has substitutes, changes in its relative price can encourage the production and consumption of other illicit and harmful drugs. This paper considers if county-level bans on the sale of alcohol in the state of Mississippi encourage the production and consumption of crystal methamphetamine. We estimate the parameters of a drug production function in which the inputs are the density of people and firms, underscoring the importance of learning and knowledge spillovers to production and consumption. Poisson and Negative Binomial parameter estimates reveal that county-level bans on hard liquor sales; but not on beer and wine, increase the number of crystal methamphetamine labs. In the absence of such laws, there would be approximately 308 fewer crystal methamphetamine labs in the state of Mississippi. Our findings suggest that in Mississippi, which is the least healthiest state in the nation, county-level bans on hard liquor sales are not welfare improving as they encourage substitution for a drug that is potentially more harmful to individual health than alcohol.


1978 ◽  
Vol 27 (1-4) ◽  
pp. 155-158
Author(s):  
S.K. Ray ◽  
Ashok Sahai

The intracta bility of Best's (1974) expression for the variance of the minimum variance unbiased (MVU) estimate of tho negative binomial parameter motivated Mikulski and Smith (1976) to find an upper bound for it. In the present paper a finer upper bound is achieved.


2009 ◽  
Vol 12 (1) ◽  
pp. 288-307 ◽  
Author(s):  
Miguel A. García-Pérez ◽  
Vicente Núñez-Antón

Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.


Sign in / Sign up

Export Citation Format

Share Document