Öz
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.
Anahtar Kelimeler
B distributions Cumulants Moments Neyman type A Pólya -Aeppli distribution Thomas distribution
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
B tipi dağılmlar Kümülantlar Momentler Neyman A Pólya –Aeppli dağılımı Thomas dağılımı
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | İstatistiksel Teori |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Ağustos 2012 |
| Yayımlandığı Sayı | Yıl 2012 Cilt: 9 Sayı: 2 |
