Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지

Conditional Skewness and Kurtosis in Natural Exponential Models

  • Published : 1998.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let T=( $T_1$,…, $T_{k}$;k$\geq$2) be a minimal sufficient and complete statistic for a k-parameter exponential model. Consider a partition of T into ( $T_1$, $T_2$), where $T_1$=( $T_1$,…, $T_{r}$ and $T_2$=( $T_{r+1}$,…, $T_{k}$1$\leq$r$\leq$k-1/). This article represents a way to obtain higher moments such as skewness and kurtosis for the distribution T and the conditional distribution of $T_1$, given $T_2$= $t_2$. These results are illustrated by some examples.s.les.s.

Keywords

References

  1. Information and Exponential Families in Statistical Theory Barndorff-Nielsen, O.
  2. Mathematical Statistics Bickel, P. J.;Doksum, K.
  3. Mathematical Statistics(4th ed.) Freund, J. E.;Walpole, R. E.
  4. The Advanced Theory of Statistics(3rd ed) v.1 Distribution Theory Kendall, M. G.;Stuart, A.
  5. Testing of point estimation Lehmann, E. L.
  6. Testing Statistical Hypothesis(2nd ed.) Lehmann, E. L.
  7. Statistical Theory, (Fourth Edition) Lindgren, B. W.
  8. Introduction to the Theory of Statistics, (Third Edition) Mood, A. M.;Graybill, F. A.;Boes, D. C.
  9. The American statistician v.48 no.2 A Derivation of conditional cumulants in Exponential Model Shaul K. B.