Journal of the Korean Statistical Society

  • 제36권3호
  • /
  • Pages.357-365
  • /
  • 2007
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

CHARACTERIZATION OF SOME CONTINUOUS DISTRIBUTIONS BY PROPERTIES OF PARTIAL MOMENTS

  • Abraham, B. (Department of Statistics and Actuarial Science, University of Waterloo) ;
  • Nair, N. Unnikrishnan (Department of Statistics, Cochin University of Science and Technology) ;
  • Sankaran, P.G. (Department of Statistics, Cochin University of Science and Technology)
  • 발행 : 2007.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we present characterizations of the Pareto, Lomax, exponential and beta models by some properties of their $r^{th}$ partial moment defined as ${\alpha}_r(t)=E[(X-t)^+]^r$, where $(X-t)^+ = max(X-t,0)$. Given the partial moments at a few truncation points, these results enable us to calculate the moments at many other points.

키워드

참고문헌

  1. ACZEL, J. (1966). Lectures on Functional Equations and Their Applications, Academic Press, New York
  2. CHONG, K. M. (1977). 'On characterizations of the exponential and geometric distributions by expectations', Journal of the American Statistical Association, 72, 160-161 https://doi.org/10.2307/2286929
  3. DENUIT, M. (2002). 'S-convex extrema, Taylor-type expansions and stochastic approximations', Scandinavian Actuarial Journal, 1, 45-67
  4. GALAMBOS, J. AND KaTZ, S. (1978). Characterization of Probability Distributions, Lecture notes in Mathematics No. 675, Springer-Verlag, Berlin
  5. GUPTA, P. L. AND GUPTA, R. C. (1983). 'On the moments of residual life in reliability and some characterization results', Communications in Statistics-Theory and Methods, 12, 449-461 https://doi.org/10.1080/03610928308828471
  6. LIN, G. D. (2003). 'Characterization ofthe exponential distribution via the residual lifetime' , Sankhyii, 65, 249-258
  7. NAIR, N. V. (1987). 'A characteristic property of the Gumbel's bivariate exponential distribution', Bulletin of Calcutta Statistical Association, 36, 181-184 https://doi.org/10.1177/0008068319870307
  8. NAIR, N. V., PRIYA, P. AND GEETHA, K. G. (2000). 'On partial moments of discrete distributions and their applications', Far East Journal of Theoretical Statistics, 4, 153-164