scholarly journals Gompertz Fréchet stress-strength Reliability Estimation

2021 ◽  
pp. 4892-4902
Author(s):  
Sarah A. Jabr ◽  
Nada S. Karam
Keyword(s):  
Maximum Likelihood ◽  
Reliability Estimation ◽  
Least Square ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Fréchet Distribution ◽  
Distribution Parameters ◽  
Estimate Reliability ◽  
Frechet Distribution ◽  
Better Than

In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.

scholarly journals Gompertz Fréchet Strength of a component between two stresses Reliability Estimation

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Sarah Adnan ◽  
Nada Sabah Karam
Keyword(s):  
Maximum Likelihood ◽  
Sampling Methods ◽  
Reliability Estimation ◽  
Least Square ◽  
Scale Parameters ◽  
Fréchet Distribution ◽  
Distribution Parameters ◽  
Component Strength ◽  
Frechet Distribution ◽  
Better Than

In this paper, the reliability of the stress-strength model is derived for probability P( <X< ) of a component strength X between two stresses ,  , when X and ,  are independent Gompertz Fréchet distribution with unknown and known shape parameters and common known scale parameters. Different methods used to estimate R and Gompertz Fréchet distribution parameters which are [Maximum Likelihood, Least square, Weighted Least square, Regression and Ranked set sampling methods], and the comparison between these estimations by simulation study based on mean square error criteria. The comparison confirms that the performance of the maximum likelihood estimator works better than the other estimators.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

scholarly journals Estimating the Reliability Function of (2+1) Cascade Model

2019 ◽  
Vol 16 (2) ◽  
pp. 0395
Author(s):  
Khaleel Et al.
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Cascade Model ◽  
Least Square ◽  
Estimation Methods ◽  
Percentage Error ◽  
Estimate Reliability ◽  
Best Estimator

This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

scholarly journals Optimality of the maximum likelihood estimator in astrometry

2018 ◽  
Vol 616 ◽  
pp. A95 ◽  
Author(s):  
Sebastian Espinosa ◽  
Jorge F. Silva ◽  
Rene A. Mendez ◽  
Rodrigo Lobos ◽  
Marcos Orchard
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Estimator ◽  
Weighted Least Squares ◽  
Least Square ◽  
Performance Limits ◽  
Likelihood Estimator ◽  
Weighted Least Square ◽  
Wide Range ◽  
Close Form

Context. Astrometry relies on the precise measurement of the positions and motions of celestial objects. Driven by the ever-increasing accuracy of astrometric measurements, it is important to critically assess the maximum precision that could be achieved with these observations. Aims. The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramér–Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a charge-coupled device (CCD)-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Methods. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. Results. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. Conclusions. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.

scholarly journals LARGE Estimation of the stress-strength reliability of progressively censored inverted exponentiated Rayleigh distributions

2017 ◽  
Vol 13 (1) ◽  
pp. 49-76 ◽  
Author(s):  
Akram Kohansal
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Scale Parameter ◽  
Sampling Technique ◽  
Credible Interval ◽  
Type Ii ◽  
Shape Parameters ◽  
Likelihood Estimator ◽  
Censored Samples

Abstract Based on progressively Type-II censored samples, this paper deals with the estimation of R = P(X < Y) when X and Y come from two independent inverted exponentiated rayleigh distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator and UMVUE of R is obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Monte Carlo simulations are performed to compare the performances of the different methods. One illustrative example is provided to demonstrate the application of the proposed method.

scholarly journals Beta Generalized Exponentiated Frechet Distribution with Applications

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 687-697
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Information Matrix ◽  
Model Parameters ◽  
Fréchet Distribution ◽  
Method Of Maximum Likelihood ◽  
Frechet Distribution ◽  
Fisher's Information

Abstract In this article we introduce a new six - parameters model called the Beta Generalized Exponentiated-Frechet (BGEF) distribution which exhibits decreasing hazard rate. Many models such as Beta Frechet (BF), Beta ExponentiatedFrechet (BEF), Generalized Exponentiated-Frechet (GEF), ExponentiatedFrechet (EF), Frechet (F) are sub models. Some of its properties including rth moment, reliability and hazard rate are investigated. The method of maximum likelihood isproposed to estimate the model parameters. The observed Fisher’s information matrix is given. Moreover, we give the advantage of the (BGEF) distribution by an application using two real datasets

Sign in / Sign up

Export Citation Format

Share Document