대한수학회지 (Journal of the Korean Mathematical Society)

  • 제39권4호
  • /
  • Pages.495-507
  • /
  • 2002
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EXPONENTIAL FAMILIES RELATED TO CHERNOFF-TYPE INEQUALITIES

  • Bor, G.R.Mohtashami (Department of Mathematics and Statistics, Faculty of Science, University of Birjand)
  • 발행 : 2002.07.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the characterization results related to Chernoff-type inequalities are applied for exponential-type (continuous and discrete) families. Upper variance bound is obtained here with a slightly different technique used in Alharbi and Shanbhag [1] and Mohtashami Borzadaran and Shanbhag [8]. Some results are shown with assuming measures such as non-atomic measure, atomic measure, Lebesgue measure and counting measure as special cases of Lebesgue-Stieltjes measure. Characterization results on power series distributions via Chernoff-type inequalities are corollaries to our results.

키워드

참고문헌

  1. J. Statist. Plann. Inference v.55 General characterization theorem based on versions of the Chernoff inequality and the Cox representation A.A.G.Alharbi;D.N.Shanbhag https://doi.org/10.1016/0378-3758(95)00191-3
  2. Statist. Probab. Lett. v.3 On upper bounds for the variance of a function of a random variable T. Cacoullos;V. Papathanasiou https://doi.org/10.1016/0167-7152(85)90014-8
  3. Math. Methods Statist. v.4 A generalization of covariance identity and related characterizations
  4. J. Statist. Plann. Inference v.63 Characterizations of distributions by generalization of variance bounds and simple proof of the CLT https://doi.org/10.1016/S0378-3758(97)00008-6
  5. Ann. Probab. v.9 A note on an inequality involving the normal distribution H. Chernoff https://doi.org/10.1214/aop/1176994428
  6. Ann. Appl. Probab. v.7 no.4 Stein's method and zero bias transformation with application to simple random sampling L. Goldstein;G. Reinert https://doi.org/10.1214/aoap/1043862419
  7. Ann. Statist. v.6 A natural identity for exponential families with applications in multi-parameter estimation H. M. Hudson https://doi.org/10.1214/aos/1176344194
  8. Statist. Probab. Lett. v.39 Further results based on Chernofftype inequalities Mohtashami Borzadaran;D.N.Shanbhag https://doi.org/10.1016/S0167-7152(98)00036-4
  9. Probability and statistical Models with applications Unified variance bounds and a Stein-type identity N. Papadatos;V. Papathanasiou;Charalambides, C.A.(ed.);Koutras, M.V.(ed.)Balakrishnan, N.(ed.)
  10. Sankhya Ser. v.A55 Characterizations of power series and factorial series distributions V. Papathanasiou
  11. J. Appl. Probab v.16 Characterizations of distributions through some identities B.L.S.Prakasa Rao https://doi.org/10.2307/3213156

피인용 문헌

  1. On generalized moment identity and its applications: a unified approach vol.50, pp.5, 2016, https://doi.org/10.1080/02331888.2015.1119150