ScholarLens Back to search
2009•Journal of Gansu Lianhe UniversityRequires access

On Distributional Properties of Order Statistic with Pareto Distribution

Nenghui Kuang

Open publisher page 0 citations

Abstract

Set {Xk,1≤k≤n} are independent and identical distributions,X(1),X(2),…,X(n) are their order statistics.When Xk is Pareto distribution with parameter r(r0),the joint probability density function of(X(1),X(2),…,X(n)) and the density functions of X(1) and X(n) are obtained.Therefore the representation formulas of the mathematical expectation and variance of X(1) and X(n) are obtained.What's more,proving that X(1),X(2),…,X(n)-X(n-1) are not independent and not identical distributions.

About this research paper

What this paper is about

Set {Xk,1≤k≤n} are independent and identical distributions,X(1),X(2),…,X(n) are their order statistics.When Xk is Pareto distribution with parameter r(r0),the joint probability density function of(X(1),X(2),…,X(n)) and the density functions of X(1) and X(n) are obtained.Therefore the representation formulas of the mathematical expectation and variance of X(1) and X(n) are obtained.What's more,proving that X(1),X(2),…,X(n)-X(n-1) are not independent and not identical distributions.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Set {Xk,1≤k≤n} are independent and identical distributions,X(1),X(2),…,X(n) are their order statistics.When Xk is Pareto distribution with parameter r(r0),the joint probability density function of(X(1),X(2),…,X(n)) and the density functions of X(1) and X(n) are obtained.Therefore the representation formulas of the mathematical expectation and variance of X(1) and X(n) are obtained.What's more,proving that X(1),X(2),…,X(n)-X(n-1) are not independent and not identical distributions.

Key concepts: Order statistic, Mathematics, Combinatorics, Pareto principle, Probability density function, Statistic, Distribution (mathematics), Joint probability distribution

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Distributional Properties of Order Statistic with Pareto Distribution — Research Paper | ScholarLens