On Some Aspects of Unbiased Estimation of Parameters in Quasi-Binomial Distributions
15 Aug 2008-Communications in Statistics-theory and Methods (Taylor & Francis Group)-Vol. 37, Iss: 19, pp 3023-3028
TL;DR: In this article, an attempt has been made to settle the question of existence of an unbiased estimator of the key parameter p of the quasi-binomial distributions of Type I (QBD I) and of Type II(QBD II), with/without any knowledge of the other parameter φ appearing in the expressions for probability functions of the QBD's.
Abstract: In this article, an attempt has been made to settle the question of existence of unbiased estimator of the key parameter p of the quasi-binomial distributions of Type I (QBD I) and of Type II (QBD II), with/without any knowledge of the other parameter φ appearing in the expressions for probability functions of the QBD's. This is studied with reference to a single observation, a random sample of finite size m as also with samples drawn by suitably defined sequential sampling rules.
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TL;DR: In this paper, a sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples and applied to infer the parameters of multidimensional or multiinomial random walks that are observed until they reach a boundary.
Abstract: A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial random walks that are observed until they reach a boundary. Clinical trials are shown to be representable within this scheme and an application to the estimation of the multinomial probabilities following multinomial clinical trials is presented.
3 citations
TL;DR: In this article, a sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples, and an application to clinical trials is presented.
Abstract: A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial Random Walks which are observed until they reach a boundary. An application to clinical trials is presented.
2 citations
Cites background from "On Some Aspects of Unbiased Estimat..."
...Further relevant results related to the main topic can be found in Bhat and Kulkarni (1966) regarding efficient multinomial sampling plans, in Sinha and Sinha (1992) for a review of the binomial case and in Sinha et al. (2008) for generalizations to the quasi-binomial context....
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References
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Book•
01 Jan 1992
TL;DR: In this paper, the authors propose a family of Discrete Distributions, which includes Hypergeometric, Mixture, and Stopped-Sum Distributions (see Section 2.1).
Abstract: Preface. 1. Preliminary Information. 2. Families of Discrete Distributions. 3. Binomial Distributions. 4. Poisson Distributions. 5. Neggative Binomial Distributions. 6. Hypergeometric Distributions. 7. Logarithmic and Lagrangian Distributions. 8. Mixture Distributions. 9. Stopped-Sum Distributions. 10. Matching, Occupancy, Runs, and q-Series Distributions. 11. Parametric Regression Models and Miscellanea. Bibliography. Abbreviations. Index.
2,106 citations
19 Aug 2005
811 citations
"On Some Aspects of Unbiased Estimat..." refers background in this paper
...Johnson et al. (1992, 2005) also mentioned QBD I and QBD II....
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Book•
01 Jan 1977
741 citations
"On Some Aspects of Unbiased Estimat..." refers methods in this paper
...Again, Consul and Mittal ( 1975 ) derived a different form of quasi-binomial distribution, known as quasi-binomial distribution of Type II (QBD II), through an urn model using four urns with pre-determined strategy and the underlying pf is given by (vide Johnson and Kotz, 1977 ):...
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332 citations