Abstract
In paper [6] J.G. Skellam gave a distribution which grew out of a compound of a binomial distribution and a beta one. In the present paper we consider an analogous problem by compounding a binomial distribution and a generalized beta one given in [8] by T. Śródka. The distribution obtained yields interesting special as well as limit cases constituting compounds of the binomial distribution and those most frequently encountered in statistical practice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dyczka, W.: Zastosowanie składania rozkładów do wyznaczania momentów (Application of compounding distributions for the calculations of moments, in Polish), Zeszyty Nauk. Polit. Łódkiej (Scient. Bull. Łódź Techn. Univ.), 168 (1973), Matematyka, Fasc. 3, pp. 205–230.
Feller, W. : An introduction to Probability Theory and Its Application, vol. II, New York 1966 , John Wiley and Sons.
Gerstenkorn, T., Śródka, T.: Kombinatoryka i rachunek prawdopodobieństwa (Combinatorics and probability theory, in Polish) , Warsaw 1980, 6th edition , Polish Scientific Publishers.
Gurland, J. : Some interrelations among compound and generalized distributions Biometrika, 44 (1957) , pp. 265–268.
Ogiński, L.: Zastosowanie pewnego uogólnionego rozkładu beta w teorii niezawodności i estymacja jego parametrów (Application of a generalized beta distribution in the reliability theory and estimation of its parameters, in Polish), Doctor thesis, Łódź Techn. Univ., Inst of Math., Łódź 1980.
Skellam, J. G. : A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials, J. Roy. Statist. Soc.Ser.B, 10, 2(1948) ,pp. 257–261.
Stacy, E. W.: A generalization of the gamma distribution, Ann. Math. Stat., 33, 3 (1962), pp. 1187–1192.
Śródka, T.: On some generalized Bessel-type probability distribution, Zeszyty Nauk. Polit. Łódź- kiej (Scient. Bull. ŁódźTechn. Univ.), 179 (1973), Matematyka, Fasc. 4, pp. 5–31.
Śródka, T.: On the distribution of product and ratio of powers of two independent random variables with the generalized gammay Maxwell and Weibull distribution, Ann. Soc. Math. Polonae, Series I: Comment. Math. (Prace Matem.), 11 (1967), pp. 77– 85.
Śródka, T„: Rozkład iloozynu potęg dwu zmiennych losowych nieżaleznych podlegających uogólnionemu rozkładowi gamma (Distribution of the product of powers of two independent random variables subject to generalized gamma distribution, in Polish, Zeszyty Nauk. Polit. Łódzkiej (Scient. Bull. Łódź Techn. Univ.), 112 (1970), Elektryka, Fasc. 31, pp. 47–66.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 D. Reidel Publishing Company
About this chapter
Cite this chapter
Gerstenkorn, T. (1982). The Compounding of the Binomial and Generalized Beta Distributions. In: Grossmann, W., Pflug, G.C., Wertz, W. (eds) Probability and Statistical Inference. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7840-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-009-7840-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7842-3
Online ISBN: 978-94-009-7840-9
eBook Packages: Springer Book Archive