zbMATH — the first resource for mathematics

On maximum likelihood estimation for count data models. (English) Zbl 0724.62103
Insur. Math. Econ. 9, No. 1, 39-49 (1990); corrigendum ibid. 10, No. 1, 81 (1991).
From the author’s summary: Based on the pseudo-compound Poisson representation of any discrete distribution defined on the positive integers, we study properties of maximum likelihood equations. Necessary and sufficient conditions are given for a moment estimator equation to be maximum likelihood.
Reviewer: A.Reich (Köln)

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F10 Point estimation
Full Text: DOI
[1] Bardwell, G.E.; Crow, E.L., A two-parameter family of hyper-Poisson distributions, J. of the amer. stat. assoc., 59, 133-141, (1964) · Zbl 0137.13301
[2] Bühlmann, H., Numerical evaluation of the compound Poisson distribution: recursion of fast Fourier transform?, Scand. actuarial journal, 116-126, (1984) · Zbl 0547.62069
[3] Chan, B., Recursive formulas for discrete distributions, Insurance: mathematics and economics, 1, 241-243, (1982) · Zbl 0494.62018
[4] Engen, S., On species frequency models, Biometrika, 51, 263-270, (1974) · Zbl 0281.62062
[5] Feller, W., An introduction to probability theory and its applications, Vol. 1, (1968), Wiley New York · Zbl 0155.23101
[6] Giffin, W.C., Transform techniques for probability modeling, (1975), Academic Press New York · Zbl 0387.90002
[7] Gossiaux, A.; Lemaire, J., Méthodes d’ajustement de distributions de sinistres, Bull. assoc. swiss actuaries, 87-95, (1981)
[8] Hürlimann, W., An elementary proof of the andelson—panjer recursion formula, Insurance: mathematics and economics, 7, 39-40, (1988) · Zbl 0657.62122
[9] Jewell, W.; Sundt, B., Further results on recursive evaluation of compound distributions, ASTIN bulletin, 12, 27-39, (1981)
[10] Johnson, N.L.; Kotz, S., Distribution in statistics: discrete distributions, (1969), Wiley New York · Zbl 0213.21101
[11] Katti, S.K., Infinite divisibility of integer-valued random variables, Annals of math. statistics, 38, 1306-1308, (1968) · Zbl 0158.17004
[12] Katti, S.K.; Rao, A.V., The log-zero-Poisson distribution, Biometrics, 26, 801-813, (1970)
[13] Kestemont, R.-M.; Paris, J., Sur l’ajustement du nombre de sinistres, Bull. assoc. swiss actuaries, 157-164, (1985)
[14] Kestemont, R.-M.; Paris, J., On compound Poisson laws, (1987), Oberwolfach West Germany, Paper presented at the meeting on Risk Theory
[15] Lamber, D.; Tierney, L., Asymptotic properties of maximum likelihood estimates in the mixed Poisson model, The annals of statistics, 12, 1388-1399, (1984) · Zbl 0562.62038
[16] Panjer, H.H.; Willmot, G.E., Motivating claim frequency models, (1988), International Congress of Actuaries Helsinki
[17] Ruohonen, M., A model for the claim number process, ASTIN bulletin, 18, (1988)
[18] Steutel, F., Preservation of infinite divisibility under mixing and related topics, Math. centre tracts, 33, (1970) · Zbl 0226.60013
[19] Van Harn, K., Classifying infinitely divisible distributions by functional equations, Math. centre tracts, 103, (1978) · Zbl 0413.60011
[20] Willmot, G.E., On the probabilities of the log-zero Poisson distribution, The Canadian J. of statistics, 15, 293-297, (1987) · Zbl 0632.62012
[21] Willmot, G.E., Sundt and Jewell’s family of discrete distributions, ASTIN bulletin, 18, (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.