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Error Estimation of Convergence of Distributions of Average of Reciprocals of Sine to the Cauchy Distribution

K. Neammanee
경북대학교 자연과학대학 수학과|2004.12|Kyungpook Mathematical Journal|제44권 제4호|pp. 537-550

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Abstract

Let X1;X2; be a sequence of independent identically distributed random variables such that sinXn 6= 0 and Fn the distribution function of 1n. nk=11sin X k . Neammanee ([7]) showed that lim n !1 Fn (x) = F(x) where F is the Cauchy distribution. In this paper, we investigate the accuracy of the approximation of F(x) to Fn (x): Under general conditions, we show that sup1 <x< 1 jFn (x) F(x)j is bounded by Cn d for 0< d <19 where C is a constant.

참고문헌 (10)

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  2. "Characteristic Functions", london (1960)
  3. "Limit distributions for random sums of reciprocals of logarithms ofindependent continuous random variables", 23(2), pp.79~100 (1998)
  4. "Limit distributions for sums of reciprocals of logarithms of absoluterandom variables", 29(2), pp.71~84 (2001)
  5. "Limit distributions for sums of reciprocals of independent randomvariables", 4(1), pp.13~28 (2002)
  6. "Limit distribution for sums of the reciprocals of sine of random variables", 43(2), pp.175~190 (2003)
  7. "Error estimates for certain probability limit theorems", 26, pp.617~630 (1955)
  8. "Domain of attraction reciprocals of power of random variables", 29, pp.734~739 (1975)
  9. "On domains of normal attraction to stable distributions", 3, pp.539~542 (1977)
  10. "Limit distributions for sums of reciprocals of independent random variables", 14, pp.281~290 (1988)

관련 논문AI추천

Limit Distribution for Sums of the Reciprocals of Sine of Random VariablesK. Neammanee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제2호Integrability and -convergence of Certain Cosine SumsJatinderdeep Kaur, Satvinder Singh Bhatia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호A central limit theorem for general weighted sums of LPQD random variables and its application고미화, 김태성, 김현철대한수학회 · 대한수학회지2006 · 제43권 제3호Conditional central limit theorems for a sequence of conditional independent random variablesDe-Mei Yuan, Lan Lei, Li-Ran Wei대한수학회 · 대한수학회지2014 · 제51권 제1호A central limit theorem for general weighted sum of LNQD random variables and its application김태성, 김현철대한수학회 · 대한수학회논문집2005 · 제20권 제3호On exact convergence rate of strong numerical schemes for stochastic differential equations남덕우대한수학회 · 대한수학회보2007 · 제44권 제1호

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