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Statistical Papers

, Volume 31, Issue 1, pp 155–159 | Cite as

On upper bounds for the characteristic values of the covariance matrix for multinomial, dirichlet and multivariate hypergeometric distributions

  • S. Huschens
Notes
  • 35 Downloads

Abstract

For the characteristic values T1 of the matrix V:=Diag(p)-ppT with p=(p1,...,pk), p1≥p2≥...≥pk≥pk+1>0 and p1+p2+...+pk+pk+1=1 the inequalities p1≥τ1≥p2≥τ2≥...≥pk≥τk>0 are given by RONNING (1982). These inequalities give, if p and pk+1 are unknown, the upper bound 1≥T1. However, in this note the bound 1/2≥T1 is derived. V is proportional to the covariance matrix for multinomial, Dirichlet and multivariate hypergeometric distributions. A statistical application for the multinomial distribution is given.

Key words

characteristic values characteristic roots covariance matrix multinomial distribution Dirichlet distribution multivariate hypergeometric distribution 

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References

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • S. Huschens
    • 1
  1. 1.Heidelberg

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