scholarly journals Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Bahman Tarvirdizade ◽  
Hossein Kazemzadeh Garehchobogh
Keyword(s):  
Maximum Likelihood ◽  
Empirical Bayes ◽  
Interval Estimation ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Bayes Estimators ◽  
Credible Sets ◽  
Lower Record ◽  
Lower Record Values ◽  
Empirical Bayes Estimators

We consider the estimation of stress-strength reliability based on lower record values when X and Y are independently but not identically inverse Rayleigh distributed random variables. The maximum likelihood, Bayes, and empirical Bayes estimators of R are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for R are obtained. A real example is presented in order to illustrate the inferences discussed in the previous sections. A simulation study is conducted to investigate and compare the performance of the intervals presented in this paper and some bootstrap intervals.

scholarly journals Interval estimation for proportional reversed hazard family based on lower record values

2015 ◽  
Vol 98 ◽  
pp. 115-122 ◽  
Author(s):  
Bing Xing Wang ◽  
Keming Yu ◽  
Frank P.A. Coolen
Keyword(s):  
Interval Estimation ◽  
Record Values ◽  
Lower Record ◽  
Lower Record Values ◽  
Family Based

scholarly journals ON ESTIMATION OF STRESS-STRENGTH RELIABILITY USING LOWER RECORD VALUES FROM ODD GENERALIZED EXPONENTIAL - EXPONENTIAL DISTRIBUTION

2021 ◽  
pp. 1-12
Author(s):  
Marwa Mohamed ◽  
Ahmed Reda
Keyword(s):  
Interval Estimation ◽  
Simulated Data ◽  
Real Data ◽  
Record Values ◽  
Point Estimation ◽  
Estimation Methods ◽  
The Real ◽  
Lower Record ◽  
Lower Record Values ◽  
Lower Records

This research paper aims to find the estimated values closest to the true values of the reliability functionunder lower record values and to know how to obtain these estimated values using point estimation methodsor interval estimation methods. This helps researchers later in obtaining values of the reliability function intheory and then applying them to reality which makes it easier for the researcher to access the missing datafor long periods such as weather. We evaluated the stress–strength model of reliability based on point andinterval estimation for reliability under lower records by using Odd Generalize Exponential–Exponentialdistribution (OGEE) which has an important role in the lifetime of data. After that, we compared theestimated values of reliability with the real values of it. We analyzed the data obtained by the simulationmethod and the real data in order to reach certain results. The Numerical results for estimated values ofreliability supported with graphical illustrations. The results of both simulated data and real data gave us thesame coverage.

scholarly journals Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fuad S. Al-Duais ◽  
Mohammed Alhagyan
Keyword(s):  
Nonlinear Programming ◽  
Loss Function ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Balanced Loss Function ◽  
Lower Record ◽  
Lower Record Values ◽  
Mean Square Errors ◽  
Balanced Loss Functions

Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

Data Processing and Technology Application in Bayes and Empirical Bayes Reliability Analysis of Parameter of Ailamujia Distribution

2014 ◽  
Vol 951 ◽  
pp. 249-252
Author(s):  
Hui Zhou
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Likelihood Estimator ◽  
Empirical Bayesian ◽  
Technology Application ◽  
Inverse Gamma ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

The estimation of the parameter of the ЭРланга distribution is discussed based on complete samples. Bayes and empirical Bayesian estimators of the parameter of the ЭРланга distribution are obtained under squared error loss and LINEX loss by using conjugate prior inverse Gamma distribution. Finally, a Monte Carlo simulation example is used to compare the Bayes and empirical Bayes estimators with the maximum likelihood estimator.

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