Compound Log-Series Distribution with Negative Multinomial Summands
The paper presents the first full characterization of multivariate random sum with one and the same Logarithmic Series number of summands in each coordinate. The summands with equal indexes in any coordinate are Negative Multinomially distributed. We show that considered as a mixture, the resulting distribution coincides with Mixed Negative Multinomial distribution with scale changed Logarithmic Series distributed first parameter.
KeywordsCompound distributions Mixed distributions Negative multinomial distribution Logarithmic series distributions
This work is partially supported by project Fondecyt Proyecto Regular No. 1151441, the Project RD-08-69/02.02.2016 from the Scientific Research Fund in Konstantin Preslavsky University of Shumen, Bulgaria and by the financial funds allocated to the Sofia University St. Kliment Ohridski, Bulgaria, grant No. 197/13.04.2016.
- 2.Fisher, R.A., Corbet, A.S., Williams, C.B.: The relation between the number of species and the number of individuals in a random sample of an animal population. J. Animal Ecol. 42–58 (1943)Google Scholar
- 3.Jose, K.K., Jacob, S.: Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis (2016)Google Scholar
- 6.Jordanova, P.K., Petkova, M.M., Stehlik, M.: Compound Power Series Distribution with Negative Multinomial Summands (2016). SubmittedGoogle Scholar
- 10.Patil, G.P.: On multivariate generalized power series distribution and its applications to the multinomial and negative multinomial. In: Proceedings of International Symposium at McGill University on Classical and Contageous Discrete Distributions, 15–20 August 1963, pp. 183–194. Statistical Publishing Society/Pergamon Press, Calcutta/Oxford (1965)Google Scholar