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Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter
Abstract
a~~2. This ~+ + YF(y+K) for K > 0, u > 0 (Anscombe, 1950). Here, u = E(Y) and K = 1/a. Also, var(Y) ,U + A2/K = A + aA2 . This distribution has numerous applications in the biological sciences [see, e.g., Breslow (1984); Margolin, Kim, and Risko (1989); and the references in Clark and Perry (1989)]. Anscombe (1950) observed that, strictly speaking, the maximum likelihood (ML) estimator of K, K, does not have a distribution, since there exists a finite probability of observing a data set from which k may not be calculated. (This occurs when the sample mean exceeds the sample variance.) A more useful parameterization involves a = 1/K, giving
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“138), are biased for small sample sizes (Pieters et al., 1977; Piegorsch, 1990; Poulin, 1996; Lloyd-Smith, 2007).”
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Metadata
- Authors
- Piegorsch, W. W.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1990-09
- Volume
- 46
- Issue
- 3
- Pages
- 863
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W237767408
- Cited by
- 177
- References
- 0
- FWCI
- 3.40
- Type
- journal article
- Language
- ca
- Open access
- closed
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