Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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The Minimum Dwell Time Algorithm for the Poisson Distribution and the Poisson-power Function Distribution

  • Kim, Joo-Hwan (Department of Computer Science & Statistics, Dongguk University, Kyong-Ju, 780-714)
  • Published : 1997.04.01
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Abstract

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

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