scholarly journals Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution

2020 ◽  
Vol 33 (4) ◽  
pp. 50
Author(s):  
Eman A.A. ◽  
Abbas N .S.
Keyword(s):  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Estimation Methods ◽  
Shrinkage Estimation ◽  
Shrinkage Estimators ◽  
Strength Model ◽  
Squared Error ◽  
Strength Models ◽  
Special Case

       A reliability system of the multi-component stress-strength model R(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown  shape parameter α and known scale parameter λ  equal to two and parameter θ equal to three. Different estimation methods of R(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

scholarly journals Preliminary test shrinkage estimators for the shape parameter of generalized exponential distribution

2016 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Abbas Najim Salman ◽  
Rana Hadi
Keyword(s):  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Preliminary Test ◽  
Shrinkage Estimators ◽  
Generalized Exponential Distribution ◽  
Initial Value ◽  
Squared Error ◽  
Optimal Region ◽  
Past Experiences

The present paper deals with the estimation of the shape parameter α of Generalized Exponential GE (α, λ) distribution when the scale parameter λ is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.Comparisons between the proposed estimator  withe classical estimator  as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)

2021 ◽  
Vol 18 (2(Suppl.)) ◽  
pp. 1103
Author(s):  
Sairan Hamza Raheem ◽  
Bayda Atiya Kalaf ◽  
Abbas Najim Salman
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Moment Method ◽  
Mean Squared Error ◽  
Rayleigh Distribution ◽  
Minimum Variance ◽  
Estimation Methods ◽  
Strength Model ◽  
Minimum Variance Unbiased Estimator ◽  
Squared Error

In this study, the stress-strength model R = P(Y < X < Z)  is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used    to estimate the parameters  namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.  

scholarly journals Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-21
Author(s):  
Talha Omer ◽  
Zawar Hussain ◽  
Muhammad Qasim ◽  
Said Farooq Shah ◽  
Akbar Ali Khan
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators ◽  
Unbiased Estimators ◽  
Squared Error ◽  
The Mean ◽  
Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

scholarly journals Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 123-140 ◽  
Author(s):  
Paulino Pérez-Rodríguez ◽  
José A. Villaseñor ◽  
Sergio Pérez ◽  
Javier Suárez
Keyword(s):  
Normal Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Posterior Distributions ◽  
Skew Normal Distribution ◽  
Inference Problems ◽  
Squared Error ◽  
Practical Standpoint ◽  
Skew Normal

The skew-normal (SN) distribution is a generalization of the normal distribution, where a shape parameter is added to adopt skewed forms. The SN distribution has some of the properties of a univariate normal distribution, which makes it very attractive from a practical standpoint; however, it presents some inference problems. Specifically, the maximum likelihood estimator for the shape parameter tends to infinity with a positive probability. A new Bayesian approach is proposed in this paper which allows to draw inferences on the parameters of this distribution by using improper prior distributions in the ``centered parametrization'' for the location and scale parameter and a Beta-type for the shape parameter. Samples from posterior distributions are obtained by using the Metropolis-Hastings algorithm. A simulation study shows that the mode of the posterior distribution appears to be a good estimator in terms of bias and mean squared error. A comparative study with similar proposals for the SN estimation problem was undertaken. Simulation results provide evidence that the proposed method is easier to implement than previous ones. Some applications and comparisons are also included.

Minimax Shrunken Technique for Estimate Burr X Distribution Shape Parameter

2018 ◽  
pp. 484
Author(s):  
Abbas Najim Salman ◽  
Maymona M. Ameen ◽  
A. E. Abdul-Nabi
Keyword(s):  
Relative Efficiency ◽  
Prior Information ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
The Real ◽  
Squared Error ◽  
Distribution Shape ◽  
Original Estimate ◽  
Bias Ratio

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.  Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.  Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.  

scholarly journals On Shrunken Estimation of Generalized Exponential Distribution

2011 ◽  
Vol 17 (64) ◽  
pp. 1
Author(s):  
عباس نجم سلمان ◽  
الاء ماجد ◽  
مها عبد الجبار
Keyword(s):  
Prior Knowledge ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Preliminary Test ◽  
Numerical Results ◽  
Generalized Exponential Distribution ◽  
Initial Value ◽  
Squared Error ◽  
Past Experiences

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a0) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge. The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about behavior of considered estimator are discussed via study the mentioned expressions. These numerical results displayed in annexed tables. Comparisons between the proposed estimator and the classical estimator as well as with some earlier studies were made to shown the effect and usefulness of the considered estimator.

scholarly journals Multicomponent Inverse Lomax Stress-Strength Reliability

2020 ◽  
pp. 72-80
Author(s):  
Nada S. Karam ◽  
Shahbaa M. Yousif ◽  
Bushra J. Tawfeeq
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Model Systems ◽  
Estimation Methods ◽  
Squared Error ◽  
Mathematical Expressions ◽  
Distribution Parameters ◽  
The Mean ◽  
Inverse Lomax Distribution

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.

Different Estimation Methods for System Reliability Multi-Components model: Exponentiated Weibull Distribution

2018 ◽  
pp. 368
Author(s):  
Abbas Najim Salman ◽  
Fatima Hadi Sail
Keyword(s):  
Weibull Distribution ◽  
System Reliability ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Independent Random Variables ◽  
Estimation Methods ◽  
Monte Carlo Simulation Technique ◽  
Squared Error ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull

        In this paper, estimation of system reliability of the multi-components in stress-strength model R(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through  Monte Carlo simulation technique were made depend on mean squared error (MSE)  criteria

scholarly journals Reducing the Bias of the Smoothed Log Periodogram Regression for Financial High-Frequency Data

Econometrics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 40
Author(s):  
Erhard Reschenhofer ◽  
Manveer K. Mangat
Keyword(s):  
Simulation Study ◽  
High Frequency ◽  
Mean Squared Error ◽  
Estimation Methods ◽  
High Frequency Data ◽  
Frequency Data ◽  
Periodic Patterns ◽  
Typical Sample ◽  
Squared Error ◽  
Proper Interpretation

For typical sample sizes occurring in economic and financial applications, the squared bias of estimators for the memory parameter is small relative to the variance. Smoothing is therefore a suitable way to improve the performance in terms of the mean squared error. However, in an analysis of financial high-frequency data, where the estimates are obtained separately for each day and then combined by averaging, the variance decreases with the sample size but the bias remains fixed. This paper proposes a method of smoothing that does not entail an increase in the bias. This method is based on the simultaneous examination of different partitions of the data. An extensive simulation study is carried out to compare it with conventional estimation methods. In this study, the new method outperforms its unsmoothed competitors with respect to the variance and its smoothed competitors with respect to the bias. Using the results of the simulation study for the proper interpretation of the empirical results obtained from a financial high-frequency dataset, we conclude that significant long-range dependencies are present only in the intraday volatility but not in the intraday returns. Finally, the robustness of these findings against daily and weekly periodic patterns is established.

Sign in / Sign up

Export Citation Format

Share Document