Advertisement

Statistical Papers

, Volume 34, Issue 1, pp 175–180 | Cite as

Some characterizations of distributions of the exponential-type

  • M. L. Targhetta
Notes

Abstract

We consider a particular subclass of the two-parameter exponential family with natural parameters γ1, γ2 and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ1 by the form of the moment generating function. As special cases we find the normal and the gamma distributions.

Key words

exponential family natural parameter space moment generating function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bildikar S., Patil G.P. (1968).Multivariate exponential type distributions. Ann. Math. Statist. 39, 1316–1326.CrossRefMathSciNetGoogle Scholar
  2. Lehmann E.L. (1983).Theory of Point Estimation. Wiley, New York.zbMATHGoogle Scholar
  3. Lukacs E. (1970).Characteristic functions. Griffin, London.zbMATHGoogle Scholar
  4. Morris C.N. (1982).Natural exponential families with quadratic variance functions. Ann. Statist. 10, 65–80.zbMATHCrossRefMathSciNetGoogle Scholar
  5. Morris C.N. (1983).Natural exponential families with quadratic variance functions: Statistical Theory. Ann. Statist. 11, 515–529.zbMATHCrossRefMathSciNetGoogle Scholar
  6. Widder D.V. (1961).Advanced Calculus. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. L. Targhetta
    • 1
  1. 1.Department of MathematicsUniversity of CagliariCagliariItaly

Personalised recommendations