Error Rate for the Limiting Poisson-power Function Distribution

  • Joo-Hwan Kim (Assistant Professor, Department of Computer Science & Statistics, Dongguk University, Kyon-ju)
  • Published : 1996.04.01

Abstract

The number of neutron signals from a neutral particle beam(NPB) at the detector, without any errors, obeys Poisson distribution, Under two assumptions that NPB scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of signals becomes a Poisson-power function distribution. In this paper, we show that the error rate in simple hypothesis testing for the limiting Poisson-power function distribution is not zero. That is, the limit of ${\alpha}+{\beta}$ is zero when Poisson parameter$\kappa\rightarro\infty$, but this limit is not zero (i.e., $\rho\ell$>0)for the Poisson-power function distribution. We also give optimal decision algorithms for a specified error rate.

Keywords

References

  1. Reviews of Modern Physics Report to The American Physical Society of the Study Group on Science and Technology of Directed Energy Weapons APS
  2. Handbook of Mathematical Functions Abramowitz, M.;Stegun, I. A.
  3. Technometrics v.29 Fitting the Student-t Distribution to Grouped Data, with Application to a Particle Scattering Experiment Beckman, R. J.;Johnson, M.
  4. LA-UR 87-3140 Discrimination with Neutral Particle Beams and Neutrons Beyer, W. A.;Qualls, C. R.
  5. An Introduction to Probability Theory and Its Applications: Volum II(Third Ed.) Feller, W.
  6. Distributions in Statistics : Continuous Univariate Distributions-I Johnson, N. L.;Kotz, S.
  7. Dongguk Journal : Natural Sciences v.33 Monotone Bayes Classification Rule on the Sample Space Kim, J. H.
  8. Dongguk Journal v.13 The Distribution of Neutral Particles with Aiming Erros Kim, J. H.
  9. '95 춘계공동학술대회논문집(II) Exact Poisson Distribution in the Use of NPB with Aiming Errors Kim, J. H.
  10. The Korean Communications in Statistics v.2 no.2 Properties of the Poisson-power Function Distribution Kim, J. H.
  11. LA-UR 87-20 NPB Aiming Error and Its Effect on Discrimination Wehner, T. R.