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.

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.

Characterization of a New Family of Distribution Through Upper Record Values

2021 ◽  
Vol 52 ◽  
Author(s):  
Md. Izhar Khan
Keyword(s):  
Conditional Expectation ◽  
Record Values ◽  
New Class ◽  
New Family ◽  
Upper Record Values ◽  
Record Value ◽  
Upper Record

In this paper, a new class of distribution has been characterized through the condi- tional expectations, conditioned on a non-adjacent upper record value. Also an equivalence between the unconditional and conditional expectation is used to characterize the new class of distribution.

Inference about Weibull Distribution Using Upper Record Values

2015 ◽  
Vol 22 (04) ◽  
pp. 1550016
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Weibull Distribution ◽  
Prediction Interval ◽  
Record Values ◽  
Testing Procedures ◽  
Scale Parameters ◽  
Upper Record Values ◽  
Record Value ◽  
Upper Record ◽  
Two Parameters ◽  
Two Parameter

This paper studies the frequentist inference about the shape and scale parameters of the two-parameter Weibull distribution using upper record values. The exact sampling distribution of the MLE of the shape parameter is derived. The asymptotic normality of the MLEs of both parameters are obtained. Based on these results this paper proposes various confidence intervals of the two parameters. Assuming one parameter is known certain testing procedures are proposed. Furthermore, approximate prediction interval for the immediately consequent record value is derived too. Conclusions are made based on intensive simulations.

scholarly journals Upper Record Values from Extended Exponential Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Devendra Kumar ◽  
Sanku Dey
Keyword(s):  
Exponential Distribution ◽  
Recurrence Relations ◽  
Shape Parameter ◽  
Record Values ◽  
Exponential Distributions ◽  
Product Moments ◽  
Conditional Moments ◽  
Upper Record Values ◽  
Upper Record

Some recurrence relations are established for the single and product moments of upper record values for the extended exponential distribution by Nadarajah and Haghighi (2011) as an alternative to the gamma, Weibull, and the exponentiated exponential distributions. Recurrence relations for negative moments and quotient moments of upper record values are also obtained. Using relations of single moments and product moments, means, variances, and covariances of upper record values from samples of sizes up to 10 are tabulated for various values of the shape parameter and scale parameter. A characterization of this distribution based on conditional moments of record values is presented.

scholarly journals Maximum observed likelihood prediction of future record values

Test ◽  
2020 ◽  
Vol 29 (4) ◽  
pp. 1072-1097 ◽  
Author(s):  
Grigoriy Volovskiy ◽  
Udo Kamps
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Record Values ◽  
Extreme Value ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Upper Record Values ◽  
Upper Record

AbstractPoint prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

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.

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