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 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 Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data

2021 ◽  
Vol 16 (2) ◽  
pp. 125-141
Author(s):  
Devendra Kumar ◽  
Mazen Nassar ◽  
Sanku Dey ◽  
Ahmed Elshahhat
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Lower Record ◽  
Lower Record Values ◽  
Dual Generalized Order Statistics ◽  
Lower Records ◽  
Highest Posterior Density ◽  
Generalized Order

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice.

scholarly journals On generalizations of the optimal choice problem

2021 ◽  
Vol 8 (1) ◽  
pp. 29-36
Author(s):  
Igor V. Belkov ◽  
Keyword(s):  
Random Variables ◽  
Initial Point ◽  
Correct Choice ◽  
Record Values ◽  
Optimal Choice ◽  
Secretary Problem ◽  
Choice Problem ◽  
Lower Record ◽  
Lower Record Values ◽  
Lower Records

The article is dedicated to some generalizations of the classical optimal choice problem (the fastidious bride problem, the secretary problem). Let there be a sequence of n identically distributed random variables on the interval [0, 1]. Getting consistently observed values of these variables, we should stop at some moment on one of them, accepting it as the initial point for counting upper or lower record values. In the optimal choice problem and its generalizations, it is needed to make the correct choice of the initial point of counting records, in order to guess the place of the last record (the classical optimal choice problem) or to maximize the expected sum of upper and/or lower record values or the expected total number of upper and/or lower records, obtained by this procedure. A review of results on the uniform distribution of the random variables and some new results concerning the exponential distribution are presented.

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 Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

scholarly journals A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

2018 ◽  
Vol 7 (5) ◽  
pp. 1
Author(s):  
Shakila Bashir ◽  
Mujahid Rasul
Keyword(s):  
Power Function ◽  
Recurrence Relations ◽  
Survival Function ◽  
Joint Probability ◽  
Record Values ◽  
Cumulative Distribution ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Lower Record ◽  
Lower Record Values

A variety of research papers have been published on record values from various continuous distributions. This paper investigated lower record values from the size-biased power function distribution (LR-SPFD). Some basic properties including moments, skewness, kurtosis, Shannon entropy, cumulative distribution function, survival function and hazard function of the lower record values from SPFD have been discussed. The joint probability density function (pdf) of $n^{th}$ and $m^{th}$ lower record values from SPFD is developed. Recurrence relations of the single and product moments of the LR-SPFD have been derived. A characterization of the lower record values from SPFD is also developed.

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