On a trivariate Poisson distribution

Sotirios Loukas; Evgenia H. Papageorgiou

Applications of Mathematics (1991)

  • Volume: 36, Issue: 6, page 432-439
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Loukas, Sotirios, and Papageorgiou, Evgenia H.. "On a trivariate Poisson distribution." Applications of Mathematics 36.6 (1991): 432-439. <http://eudml.org/doc/15691>.

@article{Loukas1991,
abstract = {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.},
author = {Loukas, Sotirios, Papageorgiou, Evgenia H.},
journal = {Applications of Mathematics},
keywords = {trivariate Poisson distribution; recurrence relationships; estimation; information matrix; maximum likelihood; simulation; partial derivatives; determinant; asymptotic covariance matrix; recurrence relations; information matrix; simulation; four parameter trivariate Poisson distribution; partial derivatives; solutions of the maximum likelihood equations; determinant; asymptotic covariance matrix; maximum likelihood estimation},
language = {eng},
number = {6},
pages = {432-439},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a trivariate Poisson distribution},
url = {http://eudml.org/doc/15691},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Loukas, Sotirios
AU - Papageorgiou, Evgenia H.
TI - On a trivariate Poisson distribution
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 6
SP - 432
EP - 439
AB - 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.
LA - eng
KW - trivariate Poisson distribution; recurrence relationships; estimation; information matrix; maximum likelihood; simulation; partial derivatives; determinant; asymptotic covariance matrix; recurrence relations; information matrix; simulation; four parameter trivariate Poisson distribution; partial derivatives; solutions of the maximum likelihood equations; determinant; asymptotic covariance matrix; maximum likelihood estimation
UR - http://eudml.org/doc/15691
ER -

References

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  1. J. T. Campbell, 10.1017/S0013091500024135, Proc. Edin. Math. Soc. 4 (1934), 18-26. (1934) Zbl0009.02801DOI10.1017/S0013091500024135
  2. P. Ноlgate, 10.1093/biomet/51.1-2.241, Biometrika 51 (1964), 241 - 245. (1964) MR0172374DOI10.1093/biomet/51.1-2.241
  3. N. L. Johnson S. Kotz, Distributions in Statistics: Discrete Distributions, Houghton Mifflin Co., Boston, 1969. (1969) MR0268996
  4. K. Kawamura, 10.2996/kmj/1138847374, Kōdai Math. Sem. Rep. 28 (1976), 1-8. (1976) Zbl0349.60013MR0428381DOI10.2996/kmj/1138847374
  5. K. Kawamura, The structure of multivariate Poisson distribution, Kōdai Math. J. 2 (1979), 337-345. (1979) Zbl0434.60019MR0553239
  6. C. D. Kemp H. Papageorgiou, Bivariate Hermite distributions, Sankhyā Ser. A 44 (1982), 269-280. (1982) MR0688806
  7. A. S. Krishnamoorthy, Multivariate binomial and Poisson distributions, Sankhyā 11 (1951), 117-124. (1951) Zbl0044.13502MR0044789
  8. S. Loukas C. D. Kemp, 10.1080/00949658308810648, J. Statist. Comput. Simul. 17 (1983), 113-123. (1983) DOI10.1080/00949658308810648
  9. D. M. Mahamunulu, 10.1080/01621459.1967.10482905, J. Amer. Statist. Assoc. 62 (1967), 251-258. (1967) Zbl0147.37802MR0216613DOI10.1080/01621459.1967.10482905
  10. H. Papageorgiou, 10.1080/03610928608829158, Commun. Statist. - Theor. Meth. 15 (1986), 893-905. (1986) Zbl0613.62021MR0832086DOI10.1080/03610928608829158
  11. C. R. Rao, Linear Statistical Inference and its Applications, Wiley, New York, 1965. (1965) Zbl0137.36203MR0221616
  12. Z. Šidák, A chain of inequalities for some types of multivariate distributions, Colloquia Mathematica Societatis János Bolyai 1972, 693 - 699. (1972) MR0370927
  13. Z. Šidák, A chain of inequalities for some types of multivariate distributions, with nine special cases, Aplikace Matematiky 18 (1973), 110-118. (1973) MR0315842
  14. Z. Šidák, On probabilities in certain multivariate distributions: Their dependence on correlations, Aplikace Matematiky 18 (1973), 128-135. (1973) MR0314197
  15. H. Teicher, On the multivariate Poisson distribution, Skand. Actuar. 37 (1954), 1 - 9. (1954) Zbl0056.35801MR0077050

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