A COMPOUND OF ZERO TRUNCATED GENERALIZED NEGATIVE BINOMIAL DISTRIBUTION WITH GENERALIZED BETA DISTRIBUTION
Keywords:
Zero truncated generalized negative binomial distribution, Generalized beta distribution, Compound distributions, Factorial and crude moments.Abstract
In this paper, we provide a chronological overview of the recent developments in the compounding of distributions. An attempt has been made to obtain a compound of zero truncated generalized negative binomial distribution (Ztgnbd) with that of Generalized Beta Distribution (GBD). Factorial and ordinary crude moments of some zero truncated compound distributions have also been discussed. The compound is then specialized by varying the value of β in ((Ztgnbd)).
Downloads
References
Ali, sajad, Aslam, Mohammed and Kazmi, Ali Mohsin (2011). Improved
informative prior for the mixture of Laplace distribution under different loss
functions, Journal of Reliability and Statistical studies, 4(2), p. 57-82
Bohlmann, G. (1913). Formulierung und Begrundung zweier Hilfssatze der
mathematischen Statistik, 14, p. 341-409.
Cekanavicius, V. and Vellaisamy, P. (2010). Compound poisson and signed
compound Poisson approximations to the Markov binomial law, 16, p. 1114-
Dubey, D.S. ( 1970). Compound gamma, beta and F distributions, Metrika.,
(1), p. 27-31.
Famoye, F. and Consul, P.C. (1992). The truncated generalized negative
binomial distribution, Journal of Applied Statistical Sciences, p. 141-157.
Gerstenkorn, T. (2004). A compound of the generalized negative binomial
distribution with the generalized beta one, CEJM, 2(4), p. 527-537.
Gerstenkorn, T. (1993). A compound of the generalized gamma distribution
with the exponential one, Bull. Soc. Sci. Letters Lodz, Vol. 43(1), Recherches
surles deformations., 16(1), p. 5-10.
Gerstenkorn, T. (1996). A compound of the Polya distribution with the beta
one, Random Oper. and Stoch. Equ., 4(2), p. 103-110.
Greenwood, M. and Yule, G.U. (1920). An inquiry into the nature of
frequency distribution representative of multiple happenings with particular
reference to the occurrence of multiple attacks of disease or of repeated
accidents, J. Roy. Stat. Soc., 83, p. 255-279.
Gurland, J. (1957). Some interrelations among compound and generalized
distributions, Biometrika, 44, p. 265-268.
Jakuszenkow, H. (1973). Nowe zlozenia rozkladow (New compounds of
distributions;in Polish), Przeglad Statystyczny, 20(1), p. 67-73.
Johnson, N.L., kotz, S. and Balakrishanan, N. (1994),Continuous Univariate
Distributiions.,John Willy& Sons, inc, New York,.
Johnson, N.L., Kotz, S. and Kemp, A. (1992). Univariate Discrete
Distributions, 2nd Ed., J. Wiley, New York.
Kaufmann, A. (1968). Introduction a la Combnatorique en Vue des
Applications, Dunold, Paris
Lukaszewicz, J and Warmus, W(1956). Metody Numertczne i Grficzne
(Numerical and Graphical Methods;in Polish), PWN, Warszawa.
Molenaar, W. (1965). Some remarks on mixtures of distributions, Bull.
Intern.Statist. Institute; 35th Session of the Intern. Statist. Inst., Beograd., 2, p.
-765.
Oginski, L. (1979). Application of a distribution of the Bessel type in
reliability theory, Polish,Matematkya, 12, p. 31-42.
Seweryn, J.G. (1986). Some probabilistic properties of Bessel distribution,
Matematkya, 19, p. 69-87.
Srodka, T. (1973). On some generalized Bessel- type probability distribution,
Matematkya, 4, p. 5-31.
