Estimation of Stress–Strength Reliability from Exponentiated Inverse Rayleigh Distribution

2019 ◽  
Vol 26 (01) ◽  
pp. 1950005 ◽  
Author(s):  
G. Srinivasa Rao ◽  
Sauda Mbwambo ◽  
P. K. Josephat
Keyword(s):  
Carbon Fibers ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Average Length ◽  
Rayleigh Distribution ◽  
Squared Error ◽  
Coverage Probabilities ◽  
Common Scale ◽  
Asymptotic Confidence Intervals ◽  
The Mean

This paper considers the estimation of stress–strength reliability when two independent exponential inverse Rayleigh distributions with different shape parameters and common scale parameter. The maximum likelihood estimator (MLE) of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error (MSE), bias, average length and coverage probabilities. Finally, a demonstration is delivered on how the proposed reliability model may be applied in data analysis of the strength data for single carbon fibers test data.

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 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 Applying the Shrinkage Technique for Estimating the Scale Parameter of Weighted Rayleigh Distribution

2020 ◽  
pp. 2335-2340
Author(s):  
Intesar Obeid Hassoun ◽  
Adel Abdulkadhim Hussein
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Squared Error ◽  
Simulation Based

This paper includes the estimation of the scale parameter of weighted Rayleigh distribution using well-known methods of estimation (classical and Bayesian). The proposed estimators were compared using Monte Carlo simulation based on mean squared error (MSE) criteria. Then, all the results of simulation and comparisons were demonstrated in tables. 

scholarly journals Estimation of the Rayleigh Distribution under Unified Hybrid Censoring

2021 ◽  
Vol 50 (1) ◽  
pp. 59-73
Author(s):  
Young Eun Jeon ◽  
Suk-Bok Kang
Keyword(s):  
Posterior Distribution ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Interval Estimation ◽  
Credible Interval ◽  
Rayleigh Distribution ◽  
Bayes Estimator ◽  
Hybrid Censoring ◽  
The Mean ◽  
Censoring Scheme

We derive some estimators of the scale parameter of the Rayleigh distribution under the unified hybrid censoring scheme. We also derive some estimators of the reliability function and the entropy of the Rayleigh distribution. First, we obtain the maximum likelihood estimator of the scale parameter. Second, we obtain the Bayes estimator using the mean of the posterior distribution. Lastly, we obtain the Bayes estimator using the mode of the posterior distribution. We also derive the interval estimation (confidence interval, credible interval, and HPD credible interval) for the scale parameter under the unified hybrid censoring scheme. We compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. Coverage probability and average lengths of 95 % and 90% intervals are obtained.

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.

scholarly journals Geometrically Convergent Simulation of the Extrema of Lévy Processes

2021 ◽  
Author(s):  
Jorge Ignacio González Cázares ◽  
Aleksandar Mijatović ◽  
Gerónimo Uribe Bravo
Keyword(s):  
Monte Carlo ◽  
Mean Squared Error ◽  
Computational Cost ◽  
Polynomial Decay ◽  
Squared Error ◽  
Locally Lipschitz ◽  
Asymptotic Confidence Intervals ◽  
Barrier Type ◽  
Optimal Computational Complexity ◽  
The Mean

We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum, and the time of the supremum of a general Lévy process at an arbitrary finite time. We identify the law of the error in simple terms. We prove that the error decays geometrically in Lp (for any [Formula: see text]) as a function of the computational cost, in contrast with the polynomial decay for the approximations available in the literature. We establish a central limit theorem and construct nonasymptotic and asymptotic confidence intervals for the corresponding Monte Carlo estimator. We prove that the multilevel Monte Carlo estimator has optimal computational complexity (i.e., of order [Formula: see text] if the mean squared error is at most [Formula: see text]) for locally Lipschitz and barrier-type functions of the triplet and develop an unbiased version of the estimator. We illustrate the performance of the algorithm with numerical examples.

Computing trade-offs in robust design: Perspectives of the mean squared error

2011 ◽  
Vol 60 (2) ◽  
pp. 248-255 ◽  
Author(s):  
Sangmun Shin ◽  
Funda Samanlioglu ◽  
Byung Rae Cho ◽  
Margaret M. Wiecek
Keyword(s):  
Robust Design ◽  
Mean Squared Error ◽  
Squared Error ◽  
Trade Offs ◽  
The Mean

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

scholarly journals Performance Analysis of AOA-Based Localization Using the LS Approach: Explicit Expression of Mean-Squared Error

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Byung-Kwon Son ◽  
Do-Jin An ◽  
Joon-Ho Lee
Keyword(s):  
Explicit Expression ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Localization Algorithm ◽  
Angle Of Arrival ◽  
Squared Error ◽  
Distance Weighted ◽  
The Mean ◽  
Passive Localization ◽  
Location Estimate

In this paper, a passive localization of the emitter using noisy angle-of-arrival (AOA) measurements, called Brown DWLS (Distance Weighted Least Squares) algorithm, is considered. The accuracy of AOA-based localization is quantified by the mean-squared error. Various estimates of the AOA-localization algorithm have been derived (Doğançay and Hmam, 2008). Explicit expression of the location estimate of the previous study is used to get an analytic expression of the mean-squared error (MSE) of one of the various estimates. To validate the derived expression, we compare the MSE from the Monte Carlo simulation with the analytically derived MSE.

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