scholarly journals Estimation of Reliability for a Two Component Survival Stress-Strength Model

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. B. Munoli ◽  
Rohit R. Mutkekar
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Strength Model ◽  
Life Testing ◽  
Likelihood Estimator ◽  
Two Component ◽  
Testing Experiment

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study.

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.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Strong Consistency of Maximum Likelihood Estimators n Exponential Sequential Model

2014 ◽  
Vol 519-520 ◽  
pp. 878-882
Author(s):  
Chang Ming Yin ◽  
Bo Hong Chen ◽  
Shuang Hua Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Strong Consistency ◽  
Maximum Likelihood Estimators ◽  
Regression Parameter ◽  
Parameter Vector ◽  
Likelihood Estimator ◽  
Sequential Model ◽  
Mild Conditions ◽  
Strongly Consistent

For the exponential sequential model, we show that maximum likelihood estimator of regression parameter vector is asymptotically existence and strongly consistent under mild conditions

Shape averages and their Bias

1994 ◽  
Vol 26 (2) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

Design problems for the pure birth process

1983 ◽  
Vol 15 (2) ◽  
pp. 255-273 ◽  
Author(s):  
Gerhard Becker ◽  
Götz Kersting
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Maximum Likelihood Estimators ◽  
Optimal Designs ◽  
Likelihood Estimator ◽  
Birth Process ◽  
Design Problems ◽  
Continuous Sampling ◽  
Optimal Procedure

Let Y(t) be a pure birth process. If a maximum likelihood estimator of the birth intensity is desired and the number n of observational points and the last observation T are given in advance, it is shown that equidistant sampling is not an optimal procedure. Properties of ‘optimal' designs and the corresponding maximum likelihood estimators are investigated and compared with equidistant and continuous sampling.

scholarly journals Classical and Bayesian Inference of Conditional Stress-Strength Model under Kumaraswamy Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Fathy H. Riad ◽  
Mohammad Mehdi Saber ◽  
Mehrdad Taghipour ◽  
M. M. Abd El-Raouf
Keyword(s):  
Bayesian Inference ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Bootstrap Method ◽  
Strength Model ◽  
Likelihood Estimator ◽  
Kumaraswamy Distribution ◽  
Strength Models

Stress-strength models have been frequently studied in recent years. An applicable extension of these models is conditional stress-strength models. The maximum likelihood estimator of conditional stress-strength models, asymptotic distribution of this estimator, and its confidence intervals are obtained for Kumaraswamy distribution. In addition, Bayesian estimation and bootstrap method are applied to the model.

Design problems for the pure birth process

1983 ◽  
Vol 15 (02) ◽  
pp. 255-273 ◽  
Author(s):  
Gerhard Becker ◽  
Götz Kersting
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Maximum Likelihood Estimators ◽  
Optimal Designs ◽  
Likelihood Estimator ◽  
Birth Process ◽  
Design Problems ◽  
Continuous Sampling ◽  
Optimal Procedure

Let Y(t) be a pure birth process. If a maximum likelihood estimator of the birth intensity is desired and the number n of observational points and the last observation T are given in advance, it is shown that equidistant sampling is not an optimal procedure. Properties of ‘optimal' designs and the corresponding maximum likelihood estimators are investigated and compared with equidistant and continuous sampling.

scholarly journals Estimating the Reliability Function for a Family of Exponentiated Distributions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ajit Chaturvedi ◽  
Anupam Pathak
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Minimum Variance ◽  
Unbiased Estimators

A family of exponentiated distributions is proposed. The problems of estimating the reliability function are considered. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are derived. A comparative study of the two methods of estimation is done. Simulation study is preformed.

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