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The mean radius of curvature of an exponential family

Author

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  • Abdelhamid, Hassairi
  • Afif, Masmoudi

Abstract

Let F=F([mu]) be the natural exponential family (NEF) on the Euclidean space generated by the measure [mu] and let k[mu]=log L[mu] be the log-Laplace transform of [mu]. In this paper, a notion of mean radius of curvature function for the NEF F is introduced using the mean radius of curvature function of the convex epigraph of the function k[mu]. An algebraic property for the variance function of F is deduced and some characteristic properties for the family F related to the mean radius of curvature function are discussed. The results are illustrated by some examples.

Suggested Citation

  • Abdelhamid, Hassairi & Afif, Masmoudi, 2001. "The mean radius of curvature of an exponential family," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 213-220, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:213-220
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