DOI QR코드

DOI QR Code

The Effects of Dispersion Parameters and Test for Equality of Dispersion Parameters in Zero-Truncated Bivariate Generalized Poisson Models

제로절단된 이변량 일반화 포아송 분포에서 산포모수의 효과 및 산포의 동일성에 대한 검정

  • Received : 20100200
  • Accepted : 20100300
  • Published : 2010.06.30

Abstract

This study, investigates the effects of dispersion parameters between two response variables in zero-truncated bivariate generalized Poisson distributions. A Monte Carlo study shows that the zero-truncated bivariate Poisson and negative binomial models fit poorly wherein the zero-truncated bivariate count data has heterogeneous dispersion parameters on dependent variables. In addition, we derive the score test for testing the equality of the dispersion parameters and compare its efficiency with the likelihood ratio test.

Keywords

Bivariate generalized Poisson distribution;bivariate negative binomial distribution;likelihood ratio test;score test;zero-truncation

References

  1. 정병철, 전희주 (2007). 제로 절단된 이변량 음이항 분포에서 독립성에 대한 검정, , 9, 2947-2957.
  2. 한상문, 정병철 (2009). 제로팽창된 이변량 음이항 분포에서 제로팽창에 대한 가설검정, , 11, 1041-1050.
  3. Charambides, C. A. (1984). Minimum variance unbiased estimation for zero class truncated bivariate poisson and logarithmic series distribution, Metrika, 31, 115-123. https://doi.org/10.1007/BF01915193
  4. Consul, P. C. (1989). Generalized Poisson Distributions: Properties and Applications, Marcel Dekker, New York.
  5. Famoye, F. and Consul, P. C. (1995). Bivariate generalized poisson distribution with some applications, Metrika, 42, 127-138. https://doi.org/10.1007/BF01894293
  6. Hamdan, M. A. (1972). Estimation in the truncated bivariate poisson distribution, Technometrics, 14, 37-45. https://doi.org/10.2307/1266916
  7. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1997). Discrete Multivariate Distributions, John Wiley & Sons, New York.
  8. Jung, B. C., Han, S. M. and Lee, J. (2007). Score tests for testing independence in the zero-truncated bivariate poisson models, Journal of Statistical Computation and Simulation, 36, 599-611.
  9. Kocherlakota, K. and Kocherlakota, S. (1985). On some tests for independence in nonnormal situations: Neyman's test, Communications in Statistics - Theory and Methods, 14, 1453-1470. https://doi.org/10.1080/03610928508828987
  10. Kocherlakota, S. and Kocherlakota, K. (1992). Bivariate Discrete Distributions, Marcel Dekker, New York.
  11. Marshall, A. W. and Olkin, I. (1990). Multivariate distributions generated from mixtures of convolution and product families, In H.W. Block, A.R. Sampson and T.H. Savits(eds), Topics in Statistical Dependence, 372-393. IMS Lecture Notes - Monograph Series, 16.
  12. Paul, S. R., Liang, K. Y. and Self, S. G. (1989). On testing departure from the binomial and multinomial assumptions, Biometrics, 45, 231-236. https://doi.org/10.2307/2532048
  13. Piperigou, V. E. and Papageorgiou, H. (2003). On truncated bivariate discrete distributions: A unified treatment, Metrika, 58, 221-233. https://doi.org/10.1007/s001840200239
  14. Subrahmaniam, K. and Subrahmaniam, K. (1973). On the estimation of the parameters in the bivariate negative binomial distribution, Journal of the Royal Statistical Society B, 35, 131-146.

Acknowledgement

Supported by : 한국학술진흥재단