scholarly journals Moments of sample extremes of order statistics from discrete uniform distribution and numerical results

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 237-241
Author(s):  
Sinan Calik ◽  
Ayse Bugatekin
Keyword(s):  
Order Statistics ◽  
Uniform Distribution ◽  
Random Variable ◽  
Numerical Results ◽  
Discrete Uniform Distribution ◽  
Discrete Uniform

In this study, the mth raw moments of sample extremes of order statistics from discrete uniform distribution are obtained. The results of sample extremes of order statistics of random variable for the independent and identically discrete uniform distribution are given. Numerical values are shown in table form

scholarly journals Probability Functions of Order Statistics from Discrete Uniform Distribution

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Ayse Metin KarakaÅŸ ◽  
S. Çalik
Keyword(s):  
Order Statistics ◽  
Uniform Distribution ◽  
Probability Function ◽  
Probability Functions ◽  
Discrete Uniform Distribution ◽  
Discrete Uniform

In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.

scholarly journals Expectation Identity of the Discrete Uniform Distribution and Its Application in the Calculations of Higher-Order Origin Moments

2021 ◽  
Author(s):  
Jia-Lei Liu ◽  
Ying-Ying Zhang ◽  
Yuan-Quan Wang
Keyword(s):  
Uniform Distribution ◽  
Linear Equations ◽  
Random Variable ◽  
Higher Order ◽  
Matrix Inversion ◽  
High Order ◽  
Discrete Uniform Distribution ◽  
Novel Method ◽  
Discrete Uniform

Abstract We provide a novel method to analytically calculate the high-order origin moments of a Discrete Uniform (DU) random variable, that is, the expectation identity method. First, the expectation identity of the DU distribution is discovered and summarized in a theorem. After that, we analytically calculate the first four origin moments and the general kth (k=1,2,…) origin moment of the DU distribution by the expectation identity method. After comparing the corresponding coefficients on both sides of an equation, we obtain a nonhomogeneous linear equations of first degree in k+1 variables. Furthermore, we have provided two ways to solve the nonhomogeneous linear equations. The first way is by matrix inversion, and the second way is by iterative solving. Moreover, the coefficients of the first ten origin moments of the DU distribution are summarized in a table. Finally, we have a proposition for special summations.

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