Inferences for the DUS-Exponential Distribution Based on Upper Record Values

2019 ◽  
Author(s):  
Ayush Tripathi ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Exponential Distribution ◽  
Record Values ◽  
Upper Record Values ◽  
Upper Record

scholarly journals Classical and Bayesian Estimation of Stress-Strength Reliability from Generalized Inverted Exponential Distribution based on Upper Records

2019 ◽  
pp. 547-561
Author(s):  
M.J.S. Khan ◽  
Bushra Khatoon
Keyword(s):  
Confidence Interval ◽  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Real Data ◽  
Credible Interval ◽  
Record Values ◽  
Minimum Variance ◽  
Squared Error Loss Function ◽  
Upper Record Values ◽  
Upper Record

This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability (R=P(X<Y)) based on upper record values from generalized inverted exponential distribution (GIED). Hassan {et al.} (2018) discussed the maximum likelihood estimator (MLE) and Bayes estimator of $R$ by considering that the scale parameter to be known for defined distribution while we consider the case when all the parameters of GIED are unknown. In the classical approach, we have discussed MLE and uniformly minimum variance estimator (UMVUE). In Bayesian approach, we have considered the Bays estimator of R by considering the squared error loss function. Further, based on upper records, we have considered the Asymptotic confidence interval based on MLE, Bayesian credible interval and bootstrap confidence interval for $R$. Finally, Monte Carlo simulations and real data applications are being carried out for comparing the performances of the estimators of R.

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 Inference for generalized exponential distribution based on generalized order statistics

2015 ◽  
Vol 4 (2) ◽  
pp. 370
Author(s):  
Eldesoky Afify
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Survival Function ◽  
Simulated Data ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Generalized Exponential Distribution ◽  
Upper Record Values ◽  
Upper Record ◽  
Generalized Order

<p>Estimation of a parameter of generalized exponential distribution (gexp) is obtained based on generalized order statistics. The maximum likelihood and Bayes methods are used for this purpose. Survival function and hazard rate are also computed. Estimation based on upper record values from generalized exponential distribution is obtained as a special case and compared by simulated data.</p>

scholarly journals Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution

2019 ◽  
Vol 4 (4) ◽  
pp. 882-894
Author(s):  
Ritu Kumari ◽  
Kalpana K. Mahajan ◽  
Sangeeta Arora
Keyword(s):  
Exponential Distribution ◽  
Simulated Data ◽  
Record Values ◽  
Data Sets ◽  
Bayes Estimators ◽  
Informative Prior ◽  
Upper Record Values ◽  
Upper Record ◽  
Hpd Intervals ◽  
Simulated Data Sets

The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose.

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>

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