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Tytuł książki

The recurrence relations for the moments of the discrete probability distributions

Autorzy

Tadeusz Gerstenkorn

Seria

Rozprawy Matematyczne tom/nr w serii: 83 wydano: 1971

Zawartość

Pełne teksty:
rm83_01.pdf

Warianty tytułu

Abstrakty

EN

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

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

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

autor
Tadeusz Gerstenkorn

Bibliografia

  • [1] E. Cansado, About moment and factorial coefficients, Bull. Inst. Internat. Statist., 35 (1957), Rio de Janeiro, pp. 77-84.
  • [2] A. T. Craig, Note on the moments of a Bernoulli distribution, Bull. Amer. Math. Soc. 15 (1934), pp. 262-264.
  • [3] A. R. Crathorne, Moments de la binomiale par rapport à l'origine, Compt. Rend. Hébd. Acad. Sci. 198 (1934), p. 1202.
  • [4] W. D. Evans, Note on the moments of a binomially distributed variate, Ann. Math. Stat., 11 (1940), pp. 106-107.
  • [5] W. Feller, Wstęp do rachunku prawdopodobieństwa, 2nd ed., Warszawa 1966, (An Introduction to Probability Theory and Its Applications, Vol. I, New York 1957).
  • [6] M. Fisz, Rachunek prawdopodobieństwa i statystyka matematyczna, 3rd ed., Warszawa 1967 (Wahrscheinlichkeitsrechnung und Matematische Statistik, Berlin 1958; Probability theory and Mathematical Statistics, 3rd ed., New York 1963).
  • [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.
  • [9] R. Frisch, Sur les semi-invariants et moments employés dans l'etude des distributions statistiques, Oslo, Skrifter of det Norske Videnskaps Academie, III, Hist.-Filos. Klasse 3.
  • [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).
  • [12] T. Gerstenkorn, Moment recurrence relations for the generalized Poisson distributions, Bull. Soc. Sci. de Łódź, 18 (1) (1967), pp. 1-3.
  • [13] T. Gerstenkorn and T. Środka, Kombinatoryka i rachunek prawdopodobieństwa, Warszawa 1967.
  • [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.
  • [24] H. D. Larsen, Moments about the arithmetic mean of a hypergeometric frequency distribution, Ann. Math. Stat. 10 (2) (1939), pp. 198-201.
  • [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.
  • [27] A. M. Mood, The distribution theory of runs, Ann. Math. Stat. 11 (1940), pp. 367-392.
  • [28] A. Noack, Class of random variables with discrete distributions, Ann. Math. Stat. 21 (1) (1950), pp. 127-132.
  • [29] K. Pearson, Peccavimus!. (Editorial), Biom. 12, parts III and IV, November 1919, pp. 259-281.
  • [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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