Bayesian Estimation in a Generalized Negative Binomial Distribution

✍ Scribed by M. N. Islam; Prof. P. C. Consul

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 373 KB
• Volume: 28
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710280302

✦ Synopsis

A generalized negative binomial (GNB) distribution W M introduced by J m and CONSUL (1971) and was modified by NEL~ON (1976). The probability function of the distribution ie defined by the function p ( z ; m, B, 0) =-P ( 1 -O)m+~z-rforz=O,l, ..., andzerootherwise, where mrO, 0-=8<1 and /3=0 or 1 PP-ZB-~. The Bayes'estimatorsfor a number of parametric functione of 8 when m and /3 are known are derived. The prior information on 8 may be given by s bets distribution, B(a, b ) , b which no subjective significance is attached. It ha8 been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayed eetimate of P(X =&) to the corresponding ML estimate and the MVU estimate for any given sample to the order n-1 for different valuee of &. w m+pz m+Bz ( 1 Key w h : Squared error loss function; Bayed estimator; Beta distribution as prior; Determination of parameters of prior distribution.