حول بعض الخصائص التوزيعية للمدى السجلي للتوزيع المنتظم

Abu Shaqfa, Mariam Nabil (2019) حول بعض الخصائص التوزيعية للمدى السجلي للتوزيع المنتظم. Masters thesis, الجامعة الإسلامية– غزة شئون البحث العلمي والدراسات العليا-ماجستير العلوم الرياضية.

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Abstract

In this thesis, we have introduced some fundamentals of statistic and a brief overview of ordered random variables, Markov chains, and entropy. We are interested in some distributional properties of the record range for a sequence fXi; i = 1; 2; 3; :::g of independent and identically distributed (iid) continuous uni- form random variables on the unit interval. This thesis mainly depends on the paper (Record Range of Uniform Distribution) (Ahsanullah, 2005a), where we provide detailed proofs of this paper's theoretical facts. More precisely, we started our study by introducing the de�nition of nth record range (Wnr); and calculating the pdf, cdf, and conditional distribution of nth record range when X0 is is a sequence of iid continuous uniform random variables. Also, we have obtained the joint pdf of mthrecord range and nth record range via a Markov chain. Then, we have discussed some distributional properties of nth record range such that the moments and calculate some special expected values such as the mean, variance, standard deviation, covariance and correlation. Moreover, we have intro- duced some nice equalities related to the moments of the record range. In addition, we calculated the entropy of nth record range and evaluate it as a function of nth. Finally, we used the results that we obtained in this research in some applications.

Item Type: Thesis (Masters)
Subjects: Q Science > QE Geology
Depositing User: أ. دارين علي أحمد حمد
Date Deposited: 23 Nov 2020 11:34
Last Modified: 23 Nov 2020 11:34
URI: http://scholar.alaqsa.edu.ps/id/eprint/2724

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