DOI QR코드

DOI QR Code

Optimal Weights for a Vector of Independent Poisson Random Variables

  • Kim, Joo-Hwan (Department of Statistics and Information Science, Dongguk University)
  • Published : 2002.12.01

Abstract

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson random variables. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $\sum\limits_{i}w_ix_i$ is to be computed and used for the test. The optimal values of $W_i$ 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 itself is used. The above three cases are considered to the situations that are without background noise and with background noise. A comparison is made of the optimal values of $W_i$ in the three cases for both situations.

Keywords

References

  1. Los Alamos National Laboratory, LA-87-3140 Discrimination with Neutral Particle Beams and Neutrons Beyer, W. A.;Qualls, C. R.
  2. An Introduction to Probability Theory and Its Applications: Volume Ⅱ(Third Ed.) Feller, W.
  3. Los Alamos National Lab., LA-UR-86-3101 Signal-to-background noise optimization for an NPB neutron detector with energy measurement capability Graves, R. E.
  4. The Korean Communications in Statistics v.2 no.2 Properties of the Poisson-Power Function Distribution Kim, Joo-Hwan
  5. The Korean Communications in Statistics v.3 no.1 Error Rate for the Limiting Prisson-power Function Distribution Kim, Joo-Hwan
  6. The Korean Communications in Statistics v.4 no.1 The Minimum Dwell Time Algorthim for the Poisson Distribution and the Poisson-power Function Distribution Kim, Joo-Hwan
  7. The Korean Communications in Statistics v.5 no.2 Monotone Likelihood Ratio Property of the Poisson Signal Distribution with Three Sources of Errors in the Parameter Kim, Joo-Hwan
  8. Testing Statistical Hypotheses(2nd Edition.) Lehmann, E. L.
  9. Introduction to Linear and Nonlinear Programming Luengerger, D. G.
  10. An Introduction to Probability Theory and Mathematical Statistics Lohatgi, V. K.