E. W. Stacy, "A generalization of the gamma distribution," Ann. Math Stat., vol. 33, no. 3, pp. 1187--1192, 1962.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....asymptotically optimal. 2 Theorem 1 and Corollary 3 demonstrate the fact mentioned in Section 1 that a wide range of key parameters (support regions) are asymptotically optimal. 3 Asymptotically Optimal Support for Generalized Gamma Densities A generalized gamma density function p(x) has the form [20] p(x) jxj expf jxj g; 1 x 1 ; where 0; 1; 1 3 2 1 2 ; 1 1 3 1 2 1 3 2 ; and 2 is the variance of the distribution. The parameters ; and are called the exponential power parameter, the power parameter, ....

E.W. Stacy, \A generalization of the gamma distribution," Ann. Math. Stat., vol. XXXIII, pp. 1187-1192, Sept. 1962.

....(q Gamma q 0 ) 1 b a Gamma 1 b [q Gamma q 0 ] 1 b Gamma1 p i a Gamma 1 b [q Gamma q 0 ] 1 b j for q q 0 . A probability density function of Q for which p( Delta) and p( Delta) belong to the same type of distribution is the generalised gamma distribution (see Stacy [13], Lienhard Meyer [7] and Johnson, Kotz Balakrishnan [5, Ch. 17] l (q Gamma q 0 j ; 4) 1 Gamma( 1 ) q Gamma q 0 ] Gamma1 exp n Gamma [q Gamma q 0 ] o I (0;1) q Gamma q 0 ) with unknown parameters 0, 0, and 0. Indeed, the probability density function of ....

E.W. Stacy. A generalization of the gamma distribution. Annals of Mathematical Statistics, 33:1187--1192, 1962.

....a 0 is the exponential decay parameter, s 2 is the variance of the distribution, s (b 1) G (b 3) a ( b 1) 2 G (b 1) a ( b 3) 2 and l = s 1 G (b 3) a ( G (b 1) a ( a . Since when a = 1, such densities reduce to the Gamma density, they are known [18] as generalized Gamma (GG) densities, and we will refer to them as such in this paper. It is shown in the Appendix A that t = 1 for all GG densities, and therefore their overload distortions are asymptotically negligible. Most commonly used densities, such as Gaussian, Laplacian, Gamma, and ....

E.W. Stacy, "A generalization of the Gamma distribution," Ann. Math. Stat., vol. XXXIII, pp.

....x 2K Gamma1 (K Gamma 1) This is a transformed gamma random variable, Y Gamma(K; where Y = DK ) 2 : This result is mentioned in Cressie (1991) page 611, in connection with tests of complete spatial randomness. More generally this is an instance of the Generalized Gamma Distribution Stacy (1962). Due to the convenient form of this distribution, Maximum Likelihood Estimation of the rate, given some observed values of DK , is easy. Given the values of DK from a homogeneous rate 2 dimensional Poisson process, the MLE of the rate of the process from this method is given by = K P n ....

Stacy, E. W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics 33, 1187--1192.

....expansion is not applicable directly to uncertainty about regression variable selection, but it could well be useful for uncertainty about the model for the baseline hazard in parametric survival analysis. Several standard failure time models (exponential, Weibull, gamma) are special cases of Stacy s (1962) generalized gamma distribution, which could be used for continuous model expansion; the generalized F distribution of Prentice (1975) would be an even more general choice. George and McCulloch (1993) have developed the Stochastic Search Variable Selection (SSVS) method, which is similar in ....

Stacy, E.W. (1962). A generalization of the gamma distribution. Ann. Math. Statist. 33, 1187--1192.

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E. W. Stacy, "A generalization of the gamma distribution," Ann. Math Stat., vol. 33, no. 3, pp. 1187--1192, 1962.

No context found.

E. W. Stacy (1962) A Generalization of the Gamma Distribution. Annals of Mathematical Statistics, 33(3): 1187--1192.

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