Exact and asymptotic distributions of vectors of column totals relate to random matrices and their approximations- I

References

• Bateman , H. 1953 . “ Higher Transcendental Function ” . Vol. 2 , New York : McGraw Hill Book Co.,Inc .
   Google Scholar
• Cramer , H. 1946 . “ Mathematical Methods of Statistics ” . Princeton, New Jersey : Princeton University Press .
   Google Scholar
• Curtiss , J.H. 1943 . Convergent Sequences of Probability Distributions . Amer. Math. Monthly , 50 : 94 – 105 .
   Google Scholar
• Feller , W. 1968 . “ An Introduction to Probability Theory and Its Applications ” . Vol. 1 , New York : John Wiley and Sons,Inc .
   Google Scholar
• Harkness W. Technical Report Department of Statistics,Michigan State University 1956
   Google Scholar
• Hodges , J.L. and LeCam , L. 1960 . The Poisson approximation to the Poisson binomial distribution . Ann. Math. Statist , 31 : 737 – 740 .
   Google Scholar
• Katz , L. 1951 . The distribution of the number of isolates in a social group . Ann. Math. Statist , 23 : 271 – 276 .
   Google Scholar
• Katz , L. and Powell , J . 1957 . Probability distributions of random variables associated with a structure of the sample space of sociometric investigations . Ann. Math. Statist , 28 : 442 – 448 .
   Google Scholar
• Knoble , H.D. 1969 . Peŕsonal communication .
   Google Scholar
• Lieberman , G.J and Owen , D.B . 1961 . “ Table of the Hypergeometric Probability Distribution ” . In Stanford Studies in Math. and Statist , Vol. III , Stanford Uiversic:; Press .
   Google Scholar
• Minton , P.D . . Distributions Related to Column Totals in Sociometric Matrices . North Carolina University . Ph.D.Thesis
   Google Scholar
• Ord , J.K . 1968 . Approximations to distribution functions which are hypergeometric series . Biometrika , 55 : 243 – 248 .
   PubMed Web of Science ®Google Scholar
• Pryor , L. 1962 . An application of probability theory to pattern recognition , Vol. III , The Pennsylvania State University . Master Thesis
   Google Scholar
• Raff , M.S . 1956 . On approximating the point binomial . J. Amer. Stutist. Assoc , 51 : 293 – 303 .
   Web of Science ®Google Scholar
• Rainville , E.D . 1960 . “ Special Functions ” . New York : Macmillan Co .
   Google Scholar
• Smeal , D.J . . An Approximation to the Distribution of Certain Random Variables Associated with a Structure of the Sample Space of Sociometric Investigations . The Pennsylvania State University
   Google Scholar
• Szego G. Orthogonal Polynomials Amer. Math. Soc Providence, Rhode Island 1967
   Google Scholar