On a trivariate Poisson distribution
Loukas, Sotirios ; Papageorgiou, Evgenia H.
Applications of Mathematics, Tome 36 (1991), p. 432-439 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined.

Publié le : 1991-01-01
Classification:  62E10,  62E15,  62F10 
@article{104480,
     author = {Sotirios Loukas and Evgenia H. Papageorgiou},
     title = {On a trivariate Poisson distribution},
     journal = {Applications of Mathematics},
     volume = {36},
     year = {1991},
     pages = {432-439},
     zbl = {0742.62012},
     mrnumber = {1134920},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104480}
}

Loukas, Sotirios; Papageorgiou, Evgenia H. On a trivariate Poisson distribution. Applications of Mathematics, Tome 36 (1991) pp. 432-439. http://gdmltest.u-ga.fr/item/104480/

J. T. Campbell The Poisson correlation function, Proc. Edin. Math. Soc. 4 (1934), 18-26. (1934) | Zbl 0009.02801

P. Ноlgate Estimation for the bivariate Poisson distribution, Biometrika 51 (1964), 241 - 245. (1964) | MR 0172374

N. L. Johnson S. Kotz Distributions in Statistics: Discrete Distributions, Houghton Mifflin Co., Boston, 1969. (1969) | MR 0268996

K. Kawamura The structure of trivariate Poisson distribution, Kōdai Math. Sem. Rep. 28 (1976), 1-8. (1976) | MR 0428381 | Zbl 0349.60013

K. Kawamura The structure of multivariate Poisson distribution, Kōdai Math. J. 2 (1979), 337-345. (1979) | MR 0553239 | Zbl 0434.60019

C. D. Kemp H. Papageorgiou Bivariate Hermite distributions, Sankhyā Ser. A 44 (1982), 269-280. (1982) | MR 0688806

A. S. Krishnamoorthy Multivariate binomial and Poisson distributions, Sankhyā 11 (1951), 117-124. (1951) | MR 0044789 | Zbl 0044.13502

S. Loukas C. D. Kemp On computer sampling from trivariate and multivariate discrete distributions, J. Statist. Comput. Simul. 17 (1983), 113-123. (1983) | Article

D. M. Mahamunulu A note on regression in the multivariate Poisson distribution, J. Amer. Statist. Assoc. 62 (1967), 251-258. (1967) | Article | MR 0216613 | Zbl 0147.37802

H. Papageorgiou Bivariate "Short" distributions, Commun. Statist. - Theor. Meth. 15 (1986), 893-905. (1986) | Article | MR 0832086 | Zbl 0613.62021

C. R. Rao Linear Statistical Inference and its Applications, Wiley, New York, 1965. (1965) | MR 0221616 | Zbl 0137.36203

Z. Šidák A chain of inequalities for some types of multivariate distributions, Colloquia Mathematica Societatis János Bolyai 1972, 693 - 699. (1972) | MR 0370927

Z. Šidák A chain of inequalities for some types of multivariate distributions, with nine special cases, Aplikace Matematiky 18 (1973), 110-118. (1973) | MR 0315842

Z. Šidák On probabilities in certain multivariate distributions: Their dependence on correlations, Aplikace Matematiky 18 (1973), 128-135. (1973) | MR 0314197

H. Teicher On the multivariate Poisson distribution, Skand. Actuar. 37 (1954), 1 - 9. (1954) | MR 0077050 | Zbl 0056.35801