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Original Articles

Some aspects of statistical inference on the lagrange (generalized) poisson distribution

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Pages 1115-1137 | Received 01 Aug 1990, Published online: 05 Jul 2007

References

  • Armitage , P. 1957 . Studies in the variability of Pock counts , 55 : 564 – 581 .
  • Box , G.E.P. 1954 . Some theorems on quadratic forms applied in the study of analysis of variance problems, I:Effect of inequalities of variance in a One-way classification . Ann. Math. Statist. , 25 : 291 – 302 .
  • Breslow , N. 1984 . Extra Poisson variation in log-linear models . Appl. Statist. , 33 : 38 – 44 .
  • Consul , P.C. and Jain , G.C. 1970 . On a generalization of Poisson distribution, abstract . Ann. Math. Statist. , 41 : 1387
  • Consul , P.C. and Shenton , L.R. 1972 . Use of Lagrange expansion for generating discrete generalized probability distributions . SIAM, J. Appl. Math. , 23 : 239 – 248 .
  • Consul , P.C. and Shoukri , M.M. 1984 . Maximum likelihood estimation of the generalized Poisson distribution . Communications in Statistics, Theory and Methods , 13 ( 2 ) : 1533 – 1547 .
  • Consul , P.C. and Shoukri , M.M. 1986 . On the negative integer moments of the generalized Poisson distribution . Communications in Statistics, Theory and Methods , 15 ( 4 ) : 1053 – 1064 .
  • Consul , P.C. 1989 . Generalized Poisson distribution , New York : Marcel Dekker Inc .
  • Cox , D.R. 1972 . The Theory of stochastic processes , London : Chapman and Hall . Miller
  • Cramér , H. 1948 . Mathematical Methods of Statistics , New Jersey : Princeton University Press .
  • Fazal , S.S. 1977 . A test for generalized Poisson distribution . Biometrical J. , 19 ( 4 ) : 245 – 251 .
  • Gart , J.J. 1964 . The analysis of Poisson regression with an application in virology . Biometrika , 51 ( 4 ) : 517 – 521 .
  • Gart , J.J. and Pettigrew , H.M. 1970 . On the conditional moments of the k-statistics for the Poisson distribution . Biometrika , 57 ( 4 ) : 661 – 664 .
  • Good , I.J. 1975 . Lagrange distributions and branching processes . SIAM, J. Appl. Math. , 28 ( 4 ) : 270 – 275 .
  • Inagaki , N. 1973 . Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator . Ann. Inst. Statist. Math. , 265 ( 4 ) : 1 – 26 .
  • Lawless , J.F. 1987 . Negative binomial and mixed Poisson regression . Canad. J. Stat. , 15 ( 4 ) : 209 – 225 .
  • McCulllagh , P. and Nelder , J.A. 1989 . Generalized Linear Models , London : Chapman and Hall .
  • McMillan , B. and Riordan , J. 1957 . A moving single server problem . Ann. Math. Stat. , 28 : 471 – 478 .
  • Moore , D.F. 1986 . Asymptotic properties of moment estimators for overdispersed counts and proportions . Biometrika , 23 : 583 – 588 .
  • Mora , M. 1986 . Classification des fonctions variance cubiques des familles esponentielles sur . R,C.R. Acad. Sc. Paris, t. 302, Serie I , 16 : 587 – 590 .
  • Moran , P.A.P. 1970 . On asymptotically optimal tests of Composite hypotheses . Biometrika , 57 : 47 – 55 .
  • Morris , C.N. 1982 . Natural exponential families with quadratic variance functions . Ann. Statist. , 10 ( 1 ) : 65 – 80 .
  • Nelder , J.A. and Wedderburn , R.W. 1972 . Generalized linear models . J.R.S.S. A , 135 ( 1 ) : 370 – 384 .
  • Neyman , J. 1959 . “ Optimal asymptotic tests of composite hypotheses ” . In Probability and Statistics , Edited by: Grenander , U. 213 – 234 . New York : Wiley .
  • Potthoff , R.F. and Whittinghill , M. 1966 . Testing for homogeneity II:The Poisson distribution . Biometrika , 53 : 183 – 190 .
  • Reid , D.B.W. , Crawley , J.F. and Rhodes , A.J. 1949 . A study of fowl pox virus titration on the chorioallantoic by the pock counting technique . J. Immunol , 63 : 165 – 171 .
  • Roizman , B. , Hoggan , M.D. and Cornfield , J. 1960 . Linear and Parabolic estimates of the titers of herpes simplex from pock counts on the chorioallantoic membrane of the developing chick embryo , Vol. 55 , 123 – 139 . Cambridge : J. Hyg. .
  • Tanner , J.C. 1961 . A derivation of Bore1 distribution . Biometrika , 40 : 222 – 224 .

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