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An Investigation on the Moments of Neyman, Pólya -Aeppli and Thomas Distributions

Year 2012, Volume: 9 Issue: 2, 41 - 47, 15.08.2012

Abstract

Neyman type A, B distributions, Pólya -Aeppli and Thomas distributions play important roles both in probability theory itself and its applications in such as biology, seismology, risk theory, and meteorology. Although there have been many studies on these distributions, the non-existence of closed forms for their probability functions restrict their usage. Hence, the moment characteristics of these distributions, such as central, non-central, factorial moments and cumulants, play an important role. In this study, Neyman type distributions, Pólya –Aeppli distribution and Thomas distribution are explained; their central, non-central, tactarial moments and cumulants are derived.

References

  • Chen, C. W., Randolph, P., Tian-Shy, L., 2005. Using CUSUM Control Schemes for Monitoring Quality Levels in Compound Poisson Production Environment: the Geometric Poisson Process. Quality Engineering, 17. 2. 207-217.
  • Gudowska-Nowak, E., Lee, R., Nasonova, E., Ritter, S., Scholz, M., 2007. Effect of LET and Track Structure on the Statistical Distribution of Chromosome Aberrations. Advances in Space Research. 39.1070-1075.
  • Meintanis, S. G., 2007. A New Goodness of Fit Test for Certain Bivariate Distributions Applicable to Traffic Accidents. Statistical Methodology. 4. 22-34.
  • Neyman, J., 1939. On a New Class of Contagious Distributions Applicable in Entomology and Bacteriology, Annals ofMathematical Statistics. 10. 35-57.
  • Özel G., İnal C., 2008. The Probability Function of the Compound Poisson Process and an Application to Aftershock Sequences. Environınetrics. 19. 79-85.
  • Özel, G., İnal, C., 2010. The Probability Function of a Geometric Poisson Distribution. Journal of Statistical Computation and Simulation, 80. 5. 479-487.
  • Özel, G., İnal, C., 2012. On the Probability Function of the First Exit Time for Generalized Poisson Processes, Pakistan Journal of Statistics. 28. 4. Basımda.
  • Panjer, H., 1981. Recursive Evaluation of a Family of Compound Distributions. ASTIN Bulletin. 12.22-26.
  • Randolph, P., Sahinoglu, M., 1995. A Stopping Rule for a Compound Poisson Random Variable, Applied Stochastic Models and Data Analysis. 11. 2. 135-143.
  • Robin, S., 2002. A Compound Poisson Model for Word Occurrences in DNA Sequences, Applied Statistics. 51. 4. 437-451.
  • Thomas, M., 1949. A Generalization of Poisson's Binomial Limit for Use in Ecology, Biometrika, 36.18-25.

Neyman, Pólya-Aeppli ve Thomas Dağılımlarının Momentleri Üzerine Bir İnceleme

Year 2012, Volume: 9 Issue: 2, 41 - 47, 15.08.2012

Abstract

Neyman A, B tipi dağılımlar, Pólya -Aeppli ve Thomas dağılımları, hem olasılık kuramında hem de biyoloji, sismoloji, risk kuramı, meteoroloji gibi birçok uygulama alanında önem taşımaktadır. Bu dağılımlar üzerine birçok çalışma yapılmasına karşın, olasılık fonksiyonlarının kapalı biçimlerine ulaşılamaması kullanımlarını da kısıtlamaktadır. Bu nedenle dağılımlara ait merkezsel, merkezsel olmayan, faktöriyel momentler ve kümülantlar gibi moment karakteristikleri önem kazanmaktadır. Bu çalışmada Neyman tipi dağılımlar, Pólya -Aeppli dağılımı ve Thomas dağılmı açıklanmış; dağılımlara ait merkezsel, merkezsel olmayan, faktöriyel momentler ve kümülantlar elde edilmiştir.

References

  • Chen, C. W., Randolph, P., Tian-Shy, L., 2005. Using CUSUM Control Schemes for Monitoring Quality Levels in Compound Poisson Production Environment: the Geometric Poisson Process. Quality Engineering, 17. 2. 207-217.
  • Gudowska-Nowak, E., Lee, R., Nasonova, E., Ritter, S., Scholz, M., 2007. Effect of LET and Track Structure on the Statistical Distribution of Chromosome Aberrations. Advances in Space Research. 39.1070-1075.
  • Meintanis, S. G., 2007. A New Goodness of Fit Test for Certain Bivariate Distributions Applicable to Traffic Accidents. Statistical Methodology. 4. 22-34.
  • Neyman, J., 1939. On a New Class of Contagious Distributions Applicable in Entomology and Bacteriology, Annals ofMathematical Statistics. 10. 35-57.
  • Özel G., İnal C., 2008. The Probability Function of the Compound Poisson Process and an Application to Aftershock Sequences. Environınetrics. 19. 79-85.
  • Özel, G., İnal, C., 2010. The Probability Function of a Geometric Poisson Distribution. Journal of Statistical Computation and Simulation, 80. 5. 479-487.
  • Özel, G., İnal, C., 2012. On the Probability Function of the First Exit Time for Generalized Poisson Processes, Pakistan Journal of Statistics. 28. 4. Basımda.
  • Panjer, H., 1981. Recursive Evaluation of a Family of Compound Distributions. ASTIN Bulletin. 12.22-26.
  • Randolph, P., Sahinoglu, M., 1995. A Stopping Rule for a Compound Poisson Random Variable, Applied Stochastic Models and Data Analysis. 11. 2. 135-143.
  • Robin, S., 2002. A Compound Poisson Model for Word Occurrences in DNA Sequences, Applied Statistics. 51. 4. 437-451.
  • Thomas, M., 1949. A Generalization of Poisson's Binomial Limit for Use in Ecology, Biometrika, 36.18-25.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Statistical Theory
Journal Section Research Articles
Authors

Gamze Özel Kadılar

Publication Date August 15, 2012
Published in Issue Year 2012 Volume: 9 Issue: 2

Cite

APA Özel Kadılar, G. (2012). Neyman, Pólya-Aeppli ve Thomas Dağılımlarının Momentleri Üzerine Bir İnceleme. İstatistik Araştırma Dergisi, 9(2), 41-47.