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The recurrence relations for the moments of the discrete probability distributions

Seria
Rozprawy Matematyczne tom/nr w serii: 83 wydano: 1971
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Warianty tytułu
Abstrakty
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CONTENTS
1. The presentation of the problem........................................................................................................ 5
1.1. Introduction.......................................................................................................................................... 5
1.2. The presentation of the known results........................................................................................... 5
2. The recurrence relations for the moments about the origin.......................................................... 10
2.1. The power series distributions........................................................................................................ 19
2.2. The Pólya distribution........................................................................................................................ 24
3. The recurrence relations for the moments about the mean of the Pólya distribution.............. 34
3.1. The first method.................................................................................................................................. 34
3.2. The second method........................................................................................................................... 38
3.3. The third method................................................................................................................................ 41
References.................................................................................................................................................. 45
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 83
Liczba stron
46
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXXXIII
Daty
wydano
1971
Twórcy
Bibliografia
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  • [7] R. Frisch, Sur les semi-invariants de Thiele, Compt. Rend. Hébd. Acad. Sci. 181 (1925), pp. 274-276.
  • [8] R. Frisch, Recurrence formulae for the moments of the point binomial, Biom. 17 (1925), pp. 165-171.
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  • [10] T. Gerstenkorn, On the formula for the moments of the Poisson distribution, Bull. Soc. Sci. de Łódź, 10, 11 (1960), pp. 1-5.
  • [11] T. Gerstenkorn, On the generalized Poisson distributions, Soc. Sci. de Łódź, 85 (1962).
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  • [14] T. Gerstenkorn, Numerische Methoden zur Anwendung der Formeln für die Momente der Wahrscheinlichkeitsverteilungen, Wissenschaftliche Zeitschrift der Technischen Hochschule Otto von Guericke in Magdeburg 13 (3, 4) (1969), pp. 213-219.
  • [15] A, Guldberg, Sur la loi de Bernoulli à deux variables et la corrélation, Compt. Rend. Hébd. Acad. Sci. 196(1933), p. 1634.
  • [16] J. A. Joseph, On the coefficients of the expansion of $X^n$, Ann. Math. Stat. 10 (3) (1939), pp. 293-296.
  • [17] A. R. Kamat, Incomplete and absolute moments of some discrete distributions, classical and contagions discrete distributions, Proceedings of the International Symposium, McGill University, Montreal, Canada, August 15th-20th 1963, edited by G. P. Patil, Statistical Publishing Socicty, Calcutta. 1966.
  • [18] M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. I — Distribution Theory, London 1958.
  • [19] W. J. Kirkham, Moments about the arithmetic mean of a binomial frequency distribution, Ann. Math. Stat. 6 (2) (1935), pp. 96-101.
  • [20] A. A. Krishnaswami Ayyangar, Note on the recurrence formulae for the moments of the point binomial, Biom. 26 (1934), pp. 262-264.
  • [21] A. A. Krishnaswami Ayyangar, A note on the incomplete moments of the hypergeometrical series, Biom. 26 (1934), pp. 264-265.
  • [22] W. Krysicki, Remarques sur la loi de Poisson, Bull. Soc. Sci. de Łódź, 8 (7) (1957), pp. 21-23.
  • [23] S. Kullback, On the Bernoulli distribution, Bull. Amer. Math. Soc. 41 (1935), pp. 857-863.
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  • [25] A. G. Laurent. Probability distributions, factorial moments, empty cell test, classical and contagions discrete distributions, Proceedings of the International Symposium, McGill University, Montreal, Canada, August 15th-20th 1963, edited by G. P. Patil, Statistical Publishing Society, Calcutta 1965, pp. 437-442.
  • [26] J. Łukaszewicz and M. Warmus, Metody numeryczne i graficzne, Warszawa 1956.
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  • [30] K. Pearson, On the moments of the hypergeometrical series, Biom. 16 (1927), pp. 157-162.
  • [31] C. Philipson, A note on moments of a Poisson probability distribution, Skand. Actuar. 46 (1963), pp. 243-247.
  • [32] J. Riordan, Moment recurrence relations for the binomial, Poisson and hypergeometric frequency distributions, Ann. Math. Stat. 8 (2) (1937), pp. 103-111.
  • [33] R. Risser and C. E. Traynard, Les Principes de la Statistique Mathématique, Livre I, Séries statistiques, Paris 1933, pp. 320-321: 2nd ed., 1957, pp. 91-100.
  • [34] V. Romanovsky, Note on the moments of a binomial $(p + q)^n$ about its mean, Biom. 15 (1923), pp. 410-412.
  • [35] V. Romanovsky, On the moments of the hypergeometrical series, Biom. 17 (1925), pp. 57-60.
  • [36] T. Śródka, Wzór rekurencyjny na momenty zwykłe w rozkładzie Pólyi, Prace Mat. 8 (2) (1964), pp. 217-220. (A recursive formula for ordinary moments in the Pólya distribution).
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