The Jacobi polynomial and some hypergeometric type distributions

  • Paul R. Milch
Article

Keywords

Negative Binomial Distribution Jacobi Polynomial Discrete Random Variable White Ball Compound Distribution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Carlitz, L. (1963). A Bilinear Generating Function for the Jacobi Polynomials,Boll. Un. Mat. Ital., (3),18.Google Scholar
  2. [2]
    Erdèlyi, A., Magnus, W., Oberhettinger, F. and Tricomi, G. F. (1953).Higher Transcendental Functions,1, New York: McGraw-Hill.Google Scholar
  3. [3]
    Hald, A. (1960). The Compound Hypergeometric Distribution and a System of Single Sampling Inspection Plans Based on Prior Distributions and Costs,Technometrics,2, 275–340.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Kemp, C. D. and Kemp, A. W. (1956). Generalized Hypergeometric Distributions,J. R. Statist. Soc., B,18, 202–211.MATHMathSciNetGoogle Scholar
  5. [5]
    Lauricella, G. (1893). Sulle Funzioni Ipergeometriche a più Variabili,Circ. Mat., Palermo, Rendiconti, Tomo7, 111–147.MATHCrossRefGoogle Scholar
  6. [6]
    Manocha, H. L. (1967) Some Bilinear Generating Functions for Jacobi Polynomials,Proc. Camb. Phil. Soc.,63, 457–459.MATHMathSciNetGoogle Scholar
  7. [7]
    Manocha, H. L. and Sharma, B. L. (1966). Some Formulae for Jacobi Polynomials,Proc. Camb. Phil. Soc.,62, 459–462.MATHMathSciNetGoogle Scholar
  8. [8]
    Milch, P. R. (1968). A Probabilistic Proof of a Formula for Jacobi Polynomials by L. Carlitz,Proc. Camb. Phil. Soc.,64, 695–698.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Mood, A. M. (1943). On the Dependence of Sampling Inspection Plans upon Population Distributions,Ann. Math. Stat.,14, 415–425.MATHMathSciNetGoogle Scholar
  10. [10]
    Sarkadi, K. (1957). On the Distribution of the Number of Exceedances,Ann. Math. Statist.,28, 1021–1023.MATHGoogle Scholar
  11. [11]
    Sarkadi, K. (1957). Generalized Hypergeometric Distributions,Publ. Math. Inst. Hung. Acad. Sci.,2, 1–2, 59–69.MathSciNetGoogle Scholar
  12. [12]
    Slater, L. J. (1966).Generalized Hypergeometric Functions. Cambridge University Press.Google Scholar
  13. [13]
    Szegö, G. (1959).Orthogonal Polynomials. New York: Amer. Math. Soc. Colloquium Publ.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1970

Authors and Affiliations

  • Paul R. Milch

There are no affiliations available

Personalised recommendations