응용통계연구 (The Korean Journal of Applied Statistics)

  • 제26권5호
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  • Pages.759-766
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  • 2013
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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두꺼운 꼬리를 갖는 연속 확률분포들의 꼬리 확률에 관하여

On Tail Probabilities of Continuous Probability Distributions with Heavy Tails

  • Yun, Seokhoon (Department of Applied Statistics, University of Suwon)
  • 투고 : 2013.07.30
  • 심사 : 2013.10.08
  • 발행 : 2013.10.31
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 두꺼운 꼬리를 갖는 확률분포들의 여러 부류에 대해서 살펴본다. 주어진 하나의 확률분포가 이들 중 어떤 부류에 속하는 지를 알려면 해당 분포의 꼬리 확률에 대한 (점근) 표현식을 알아야만 한다. 그러나 대다수의 절대 연속 확률분포들은 분포함수가 아닌 확률밀도함수로 명시되기 때문에 통상적으로 이들의 꼬리 확률에 대한 표현식을 얻는 작업은 그리 쉬운 일이 아니다. 본 논문에서는 이러한 경우 확률밀도함수만을 이용하여 꼬리 확률에 대한 점근 표현식을 쉽게 얻을 수 있는 하나의 방법을 제안한다. 또한 제안한 방법을 설명하기 위하여 몇가지 예를 첨부한다.

The paper examines several classes of probability distributions with heavy tails. An (asymptotic) expression for tail probability needs to be known to understand which class a given probability distribution belongs to. It is usually not easy to get expressions for tail probabilities since most absolutely continuous probability distributions are specified by probability density functions and not by distribution functions. The paper proposes a method to obtain asymptotic expressions for tail probabilities using only probability density functions. Some examples are given to illustrate the proposed method.

키워드

참고문헌

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