A Characterization of the Gumbel Distribution Based on Record Values

2003 ◽  
Vol 32 (11) ◽  
pp. 2101-2108 ◽  
Author(s):  
A. A. AlZaid ◽  
M. Ahsanullah
Keyword(s):  
Gumbel Distribution ◽  
Record Values

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals Objective Bayesian Prediction of Future Record Statistics Based on the Exponentiated Gumbel Distribution: Comparison with Time-Series Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1443
Author(s):  
Yongku Kim ◽  
Jung In Seo
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Information Matrix ◽  
Simple Algorithm ◽  
Gumbel Distribution ◽  
Real Data ◽  
Good Alternative ◽  
Record Values ◽  
Shape Parameters ◽  
Record Statistics

The interest in the study of record statistics has been increasing in recent years in the context of predicting stock markets and addressing global warming and climate change problems such as cyclones and floods. However, because record values are mostly rare observed, its probability distribution may be skewed or asymmetric. In this case, the Bayesian approach with a reasonable choice of the prior distribution can be a good alternative. This paper presents an objective Bayesian method for predicting future record values when observed record values have a two-parameter exponentiated Gumbel distribution with the scale and shape parameters. For objective Bayesian analysis, objective priors such as the Jeffreys and reference priors are first derived from the Fisher information matrix for the scale and shape parameters, and an analysis of the resulting posterior distribution is then performed to examine its properness and validity. In addition, under the derived objective prior distributions, a simple algorithm using a pivotal quantity is proposed to predict future record values. To validate the proposed approach, it was applied to a real dataset. For a closer examination and demonstration of the superiority of the proposed predictive method, it was compared to time-series models such as the autoregressive integrated moving average and dynamic linear model in an analysis of real data that can be observed from an infinite time series comprising independent sample values.

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