scholarly journals Generalized Residual Entropy and Upper Record Values

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Suchandan Kayal
Keyword(s):  
Lower Bounds ◽  
Random Variable ◽  
Record Values ◽  
Lifetime Distribution ◽  
Upper And Lower Bounds ◽  
Residual Entropy ◽  
Weighted Version ◽  
Comparison Results ◽  
Upper Record Values ◽  
Upper Record

In this communication, we deal with a generalized residual entropy of record values and weighted distributions. Some results on monotone behaviour of generalized residual entropy in record values are obtained. Upper and lower bounds are presented. Further, based on this measure, we study some comparison results between a random variable and its weighted version. Finally, we describe some estimation techniques to estimate the generalized residual entropy of a lifetime distribution.

Record values and extreme value distributions

1982 ◽  
Vol 19 (01) ◽  
pp. 233-239 ◽  
Author(s):  
H. N. Nagaraja
Keyword(s):  
Random Variable ◽  
Record Values ◽  
Canonical Representation ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Upper Record Values ◽  
Lower Record ◽  
Record Value ◽  
Upper Record

The limit distribution of thekth maximum from a random sample of sizenwhenn →∞ is identified as the distribution of thekth lower record value from one of three extreme value distributions. This fact is used in giving a different canonical representation and new proofs of the results of Hall (1978) for this limiting random variable. A characterization of the exponential distribution based on upper record values is given.

Lower bounds on the expectations of upper record values

2011 ◽  
Vol 141 (8) ◽  
pp. 2726-2737 ◽  
Author(s):  
Agnieszka Goroncy ◽  
Tomasz Rychlik
Keyword(s):  
Lower Bounds ◽  
Record Values ◽  
Upper Record Values ◽  
Upper Record

Record values and extreme value distributions

1982 ◽  
Vol 19 (1) ◽  
pp. 233-239 ◽  
Author(s):  
H. N. Nagaraja
Keyword(s):  
Random Variable ◽  
Record Values ◽  
Canonical Representation ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Upper Record Values ◽  
Lower Record ◽  
Record Value ◽  
Upper Record

The limit distribution of the k th maximum from a random sample of size n when n → ∞ is identified as the distribution of the k th lower record value from one of three extreme value distributions. This fact is used in giving a different canonical representation and new proofs of the results of Hall (1978) for this limiting random variable. A characterization of the exponential distribution based on upper record values is given.

scholarly journals Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix

2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah
Keyword(s):  
Order Statistics ◽  
Condition Number ◽  
Record Values ◽  
Distributional Properties ◽  
Upper Record Values ◽  
Upper Record

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

scholarly journals Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Wen-Chuan Lee ◽  
Jong-Wuu Wu ◽  
Ching-Wen Hong ◽  
Shie-Fan Hong
Keyword(s):  
Loss Function ◽  
Performance Index ◽  
Resource Planning ◽  
Record Values ◽  
Testing Procedure ◽  
Assessment System ◽  
Squared Error Loss Function ◽  
Lifetime Performance ◽  
Upper Record Values ◽  
Upper Record

Quality management is very important for many manufacturing industries. Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, the lifetime performance indexCLis utilized to measure the performance of product, whereLis the lower specification limit. This study constructs a Bayesian estimator ofCLunder a Rayleigh distribution with the upper record values. The Bayesian estimations are based on squared-error loss function, linear exponential loss function, and general entropy loss function, respectively. Further, the Bayesian estimators ofCLare utilized to construct the testing procedure forCLbased on a credible interval in the condition of knownL. The proposed testing procedure not only can handle nonnormal lifetime data, but also can handle the upper record values. Moreover, the managers can employ the testing procedure to determine whether the lifetime performance of the Rayleigh products adheres to the required level. The hypothesis testing procedure is a quality performance assessment system in enterprise resource planning (ERP).

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