Pareto Dağılımının Koşullu Sıra İstatistiklerinin Momentleri

Year 2017, Volume 10, Issue 1, 40 - 48, 25.06.2017

Fahrettin ÖZBEY

Abstract

Bu çalışmada, Pareto dağılımının bazı özellikleri ifade edildikten sonra sıra istatistikleri incelendi. Pareto dağılımının momentleri, Pareto dağılımının sıra istatistiklerinin momentleri ve Pareto dağılımının koşullu sıra istatistiklerinin momentleri araştırıldı. Sonuç olarak bu momentlerin bazı nümerik değerleri karşılaştırıldı.

Keywords

Sıra İstatistikleri, Pareto Dağılımı, Momentler.

Moments of Conditional Order Statistics of Pareto Distribution

Abstract

In this study, some properties of Pareto distribution are expressed, then, order statistics of this distribution are examined. The moments of Pareto distribution, moments of order statistics of Pareto distribution and moments of conditional order statistics of Pareto distribution are investigated. Consequently, some numerical values of these moments are compared.

Keywords

Order Statistics, Pareto Distributions, Moments.

References

• [1] E. d-E. Afify, 2006, Order statistics from Pareto distributions, Journal of Applied Science, 6, 2151-2157.
• [2] B. C. Arnold, 2015, Pareto Distributions, John Wiley and Sons Inc. New York.
• [3] N. Balakrishnan, P. C. Joshi, 1982, Moments of order statistics from doubly truncated Pareto distribution, Journal of Indian Statistical Association, 20, 109-117.
• [4] N. Balakrishnan, H. J. Malik, S. E. Ahmed, 1988, Recurrence relations and identities for moments order statistics, Communications in Statistics – Theory and Methods, 17, 2657-2694.
• [5] A. Childs, N. Balakrishnan, 1988, Generalized recurrence relations for moments order statistics from non-identical Pareto and truncated Pareto random variables with applications to robustness, Handbook of Statistics, 16, 403-438.
• [6] H. A. David, 1981, Order Statistics, John Wiley and Sons Inc. New York.
• [7] O. L. Gebizlioğlu, S. Yörübulut, 2016, A Pseudo-Pareto distribution and concomitants of its order statistics, Methodology and Computing in Applied Probability, 18, 1043–1064.
• [8] G. Gökdere, 2014, Computing the moments of order statistics from truncated Pareto distributions based on conditional expectation, Pakistan Journal of Statistics and Operation Research, 10, 9-15.
• [9] G. Gökdere, F. Özbey, 2013, Computing the moments of Pareto order statistics, International Journal of Agricultural and Statistical Sciences, 9, 35-44.
• [10] M. Güngör, F. Özbey, 2010, Distributions of order statistics arising from non-identical continuous variables, İstatistikçiler Dergisi, 3, 63-68.
• [11] N. L. Johnson, S. Kotz, N. Balakrishnan, 1994, Continuous Univariate Distributions Vol. 1, 2nd Ed., John Wiley and Sons Inc., Hoboken.
• [12] P. C. Joshi, N. Balakrishnan,1982, Recurrence relations and identities for the product moment of order statistics, Shankya B, 44, 39-49.
• [13] Z. M. Nofal, Y. M. El Gebaly, 2017, New Characterizations of the Pareto Distribution, Pakistan Journal of Statistics and Operation Research, 13, 63-74.
• [14] V. Pareto, 1897, Cours d’economie Politique, Vol II, F. Rouge, Lausanne.
• [15] C. Taşdemir, 2016, Sıra İstatistiklerinin Şartlı Dağılımlarının Beklenen Değerleri, Yüksek Lisans Tezi, Bitlis Eren Üniversitesi Fen Bilimleri Enstitüsü, Bitlis.