Higher order moments of order statistics from INID exponential random variables

2003 ◽  
Vol 44 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Aaron Childs
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Higher Order ◽  
Higher Order Moments ◽  
Exponential Random Variables ◽  
Moments Of Order Statistics

scholarly journals Higher Order Moments of the Order Statistics for the Rectangular, Exponential, Gamma and Weibull Distributions

2021 ◽  
Vol 2 (3) ◽  
pp. 61-76
Author(s):  
Sampath Kumar ◽  
V. V. HaraGopal
Keyword(s):  
Image Analysis ◽  
Order Statistics ◽  
Order Statistic ◽  
Higher Order ◽  
Weibull Distributions ◽  
Higher Order Moments

In this paper we discuss the problem of Higher Order Moments for the order Statistics for the Rectangular, Exponential, Gamma and Weibull distributions by finding the order statistic distributions for the base distribution and modified distributions, the base distribution is to deduce the corresponding distribution by the polynomial modifier. These higher order moments are very much useful in most of the Data sciences and Image analysis.  

COMMENTS ON THE SURVEY BY BALAKRISHNAN AND ZHAO

2013 ◽  
Vol 27 (4) ◽  
pp. 445-449 ◽  
Author(s):  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Negative Binomial ◽  
Random Variables ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Exponential Random Variables ◽  
Binomial Random Variables

N. Balakrishnan and Peng Zhao have prepared an outstanding survey of recent results that stochastically compare various order statistics and some ranges based on two collections of independent heterogeneous random variables. Their survey focuses on results for heterogeneous exponential random variables and their extensions to random variables with proportional hazard rates. In addition, some results that stochastically compare order statistics based on heterogeneous gamma, Weibull, geometric, and negative binomial random variables are also given. In particular, the authors of have listed some stochastic comparisons that are based on one heterogeneous collection of random variables, and one homogeneous collection of random variables. Personally, I find these types of comparisons to be quite fascinating. Balakrishnan and Zhao have done a thorough job of listing all the known results of this kind.

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