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

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

Gamze Özel Kadılar

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.

Keywords

B distributions, Cumulants, Moments, Neyman type A, Pólya -Aeppli distribution, Thomas distribution

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

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.

Keywords

B tipi dağılmlar, Kümülantlar, Momentler, Neyman A, Pólya –Aeppli dağılımı, Thomas dağılımı

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