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2000 | 27 | 4 | 403-410
Tytuł artykułu

Variance upper bounds and a probability inequality for discrete α-unimodality

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Variance upper bounds for discrete α-unimodal distributions defined on a finite support are established. These bounds depend on the support and the unimodality index α. They increase as the unimodality index α increases. More information about the underlying distributions yields tighter upper bounds for the variance. A parameter-free Bernstein-type upper bound is derived for the probability that the sum S of n independent and identically distributed discrete α-unimodal random variables exceeds its mean E(S) by a positive value nt. The bound for P{S-nμ ≥ nt} depends on the range of the summands, the sample size n, the unimodality index α and the positive number t.
Rocznik
Tom
27
Numer
4
Strony
403-410
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-30
poprawiono
2000-02-07
Twórcy
autor
  • Department of Mathematics, King Khalid University, Abha, P.O. Box 157, Saudi Arabia
Bibliografia
  • A. M. Abouammoh and A. F. Mashhour (1983), On characterization of discrete unimodality: a survey, in: Developments in Statistics and its Applications, KSU Libraries, 327-342.
  • A. M. Abouammoh, A. M. Ali and A. F. Mashhour (1994), On characterizations and variance bounds of discrete α-unimodality, Statist. Papers 35, 151-161.
  • A. M. Abouammoh and A. F. Mashhour (1994), Variance upper bounds and convolutions of α-unimodal distributions, Statist. Probab. Lett. 21, 281-289.
  • M. H. Alamatsaz (1985), A note on an article by Artikis, Acta Math. Hungar. 45, 159-162.
  • S. W. Dharmadhikari and K. Jogdeo (1986), Some results on generalized unimodality and an application to Chebyshev's inequality, in: Reliability and Quality Control, Elsevier, 127-132.
  • S. W. Dharmadhikari and K. Joag-Dev (1989), Upper bounds for the variances of certain random variables, Comm. Statist. Theory Methods 18, 3235-3247.
  • M. I. Jacobson (1969), The maximum variance of restricted unimodal distributions, Ann. Math. Statist. 40, 1746-1752.
  • J. Muilwijk (1966), Note on a theorem of M. N. Murthy and V. K. Sethi, Sankhyā Ser. B 28, 183.
  • S. E. Navard, J. W. Seaman and D. M. Young (1993), A characterization of discrete unimodality with applications to variance upper bounds, Ann. Inst. Statist. Math. 45, 603-614.
  • R. A. Olshen and L. J. Savage (1970), A generalized unimodality, J. Appl. Probab. 7, 21-34.
  • J. C. W. Rayner (1975), Variance bounds, Sankhyā Ser. B 37, 135-138.
  • J. W. Seaman, P. L. Odell and D. N. Young (1985), Maximum variance for unimodal distributions, Statist. Probab. Lett. 3, 255-260.
  • J. W. Seaman, D. M. Young and D. W. Turner (1987), On the variance of certain bounded random variables, Math. Sci. 12, 109-116.
  • F. W. Steutel (1988), Note on discrete α-unimodality, Statist. Neerlandica 42, 137-140.
  • D. M. Young, J. W. Seaman, D. W. Turner and V. R. Marco (1988), Probability inequalities for continuous unimodal random variables with finite support, Comm. Statist. Theory Methods 17, 3505-3519.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i4p403bwm
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