• Title, Summary, Keyword: the tail probability

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The UMVUE and MLE of the Tail Probability in Discrete Model

  • Woo, Jung-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.4
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    • pp.1405-1412
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    • 2006
  • We shall derive the UMVUE of the tail probability in Poisson, Binomial, and negative Binomial distributions, and compare means squared errors of the UMVUE and the MLE of the tail probability in each case.

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A NOTE ON THE SEVERITY OF RUIN IN THE RENEWAL MODEL WITH CLAIMS OF DOMINATED VARIATION

  • Tang, Qihe
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.663-669
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    • 2003
  • This paper investigates the tail asymptotic behavior of the severity of ruin (the deficit at ruin) in the renewal model. Under the assumption that the tail probability of the claimsize is dominatedly varying, a uniform asymptotic formula for the tail probability of the deficit at ruin is obtained.

On Tail Probabilities of Continuous Probability Distributions with Heavy Tails (두꺼운 꼬리를 갖는 연속 확률분포들의 꼬리 확률에 관하여)

  • Yun, Seokhoon
    • The Korean Journal of Applied Statistics
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    • v.26 no.5
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    • pp.759-766
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    • 2013
  • 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.

Inference on Reliability in an Exponentiated Uniform Distribution

  • Lee, Chang-Soo;Won, Ho-Yon
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.2
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    • pp.507-513
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    • 2006
  • We shall consider an inference of the reliability and an estimation of the right-tail probability in an exponentiated uniform distribution. And we shall compare numerically efficiencies for proposed estimators of the scale parameter and right-tail probability in the small sample sizes.

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Tail Probability Approximations for the Ratio of two Independent Sequences of Random Variables

  • Cho, Dae-Hyeon
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.415-428
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    • 1999
  • In this paper, we study the saddlepoint approximations for the ratio of two independent sequences of random variables. In Section 2, we review the saddlepoint approximation to the probability density function. In section 3, we derive an saddlepoint approximation formular for the tail probability by following Daniels'(1987) method. In Section 4, we represent a numerical example which shows that the errors are small even for small sample size.

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On Reliability and UMVUE of Right-Tail Probability in a Half-Normal Variable

  • Woo, Jung-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.1
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    • pp.259-267
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    • 2007
  • We consider parametric estimation in a half-normal variable and a UMVUE of its right-tail probability. Also we consider estimation of reliability in two independent half-normal variables, and derive k-th moment of ratio of two same variables.

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Tail Probability Approximations for the Ratio of the Independent Random Variables

  • Cho, Dae-Hyeon
    • Journal of the Korean Data and Information Science Society
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    • v.7 no.2
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    • pp.189-201
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    • 1996
  • In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the density. And in Section 3, we derive two approximation formulae for the tail probability, one by following Daniels'(1987) method and the other by following Lugannani and Rice's (1980). In Section 4, we represent some numerical examples which show that the errors are small even for small sample size.

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Notes on the Ratio and the Right-Tail Probability in a Log-Laplace Distribution

  • Woo, Jung-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.4
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    • pp.1171-1177
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    • 2007
  • We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

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