Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Optimal Weights of Linear Combinations of the Independent Poisson Signals for Discrimination

  • Kim, Joo-Hwan (Department of Statistics and Information Science, Dongguk University)
  • Published : 2002.10.31
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Abstract

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson signals. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $$\sum\limits_{i}\omega_ix_i$$ is to be computed and used for the test. The optimal values of $\omega_i$ are calculated for three cases : (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution it self is used. A comparison is made of the optimal values of $\omega_i$ in the three cases as parameter goes to infinity.

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References

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