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ON THE MOMENTS OF ORDER STATISTICS FROM DISCRETE DISTRIBUTIONS

Sinan Çalık, Mehmet Güngör, Cemil Çolak

Open publisher page 4 citations

Abstract

In this paper, the th m raw moments of order statistics from discrete distributions are obtained. By using the th m raw moments, a relation between the moments of sample maximum of order statistics from a discrete uniform distribution and the sum   1, S N n  is obtained. It is shown that with the help of this relation, one can obtain all the moments for sample maximum of order statistics from a discrete uniform distribution. By using MATLAB, we compute the means and variances of the sample maximum order statistics for sample size N = 10(10)50(50)100 and n = 1(1)10. Further studies may focus on a software program computing the means and variances of sample maximum of order statistics from any discrete distributions.

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What this paper is about

In this paper, the th m raw moments of order statistics from discrete distributions are obtained. By using the th m raw moments, a relation between the moments of sample maximum of order statistics from a discrete uniform distribution and the sum   1, S N n  is obtained. It is shown that with the help of this relation, one can obtain all the moments for sample maximum of order statistics from a discrete uniform distribution. By using MATLAB, we compute the means and variances of the sample maximum order statistics for sample size N = 10(10)50(50)100 and n = 1(1)10. Further studies may focus on a software program computing the means and variances of sample maximum of order statistics from any discrete distributions.

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Available abstract

In this paper, the th m raw moments of order statistics from discrete distributions are obtained. By using the th m raw moments, a relation between the moments of sample maximum of order statistics from a discrete uniform distribution and the sum   1, S N n  is obtained. It is shown that with the help of this relation, one can obtain all the moments for sample maximum of order statistics from a discrete uniform distribution. By using MATLAB, we compute the means and variances of the sample maximum order statistics for sample size N = 10(10)50(50)100 and n = 1(1)10. Further studies may focus on a software program computing the means and variances of sample maximum of order statistics from any discrete distributions.

Key concepts: L-moment, Order statistic, Statistics, Mathematics, Central moment, Sample (material), Method of moments (probability theory), Distribution (mathematics)

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