scholarly journals On Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution

2021 ◽  
pp. 4847-4858
Author(s):  
Emad Sh. M. Haddad ◽  
Feras Sh. M. Batah
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Estimation Method ◽  
Reliability Function ◽  
Ordinary Least Squares ◽  
Estimation Methods ◽  
Shrinkage Estimation ◽  
Strength Model ◽  
Shrinkage Methods ◽  
Mathematical Formulas

The stress – strength model is one of the models that are used to compute reliability. In this paper, we derived mathematical formulas for the reliability of the stress – strength model that follows Rayleigh Pareto (Rayl. – Par) distribution. Here, the model has a single component, where strength Y is subjected to a stress X, represented by moment, reliability function, restricted behavior, and ordering statistics. Some estimation methods were used, which are the maximum likelihood, ordinary least squares, and two shrinkage methods, in addition to a newly suggested method for weighting the contraction. The performance of these estimates was studied empirically by using simulation experimentation that could give more varieties for different-sized samples for stress and strength. The most interesting finding indicates the superiority of the proposed shrinkage estimation method.

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.

Different inference approaches for the estimators of the sushila distribution

2021 ◽  
Vol 16 (4) ◽  
pp. 251-260
Author(s):  
Marcos Vinicius de Oliveira Peres ◽  
Ricardo Puziol de Oliveira ◽  
Edson Zangiacomi Martinez ◽  
Jorge Alberto Achcar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Bayesian Method ◽  
Weighted Least Squares ◽  
Computational Cost ◽  
Estimation Method ◽  
Computation Time ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Estimation Methods

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost.

scholarly journals E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 626
Author(s):  
Abdalla Rabie ◽  
Junping Li
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Real Life ◽  
Estimation Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Type Ii ◽  
Credible Intervals ◽  
Generalized Type

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

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 A Bi-Level Weibull Model with Applications to Two Ordered Events

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Shuguang Song ◽  
Hanlin Liu ◽  
Mimi Zhang ◽  
Min Xie
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Random Variable ◽  
Weibull Model ◽  
Reliability Function ◽  
The Other ◽  
Regularity Conditions ◽  
Maximum Likelihood Estimation Method

In this paper, we propose and study a new bivariate Weibull model, called Bi-levelWeibullModel, which arises when one failure occurs after the other. Under some specific regularity conditions, the reliability function of the second event can be above the reliability function of the first event, and is always above the reliability function of the transformed first event, which is a univariate Weibull random variable. This model is motivated by a common physical feature that arises fromseveral real applications. The two marginal distributions are a Weibull distribution and a generalized three-parameter Weibull mixture distribution. Some useful properties of the model are derived, and we also present the maximum likelihood estimation method. A real example is provided to illustrate the application of the model.

scholarly journals Comparison between the maximum likelihood and the bayesian estimation methods for logistic regression model (case study: risk of low birth weight in Indonesia)

2021 ◽  
Vol 2106 (1) ◽  
pp. 012001
Author(s):  
P R Sihombing ◽  
S R Rohimah ◽  
A Kurnia
Keyword(s):  
Logistic Regression ◽  
Birth Weight ◽  
Maximum Likelihood ◽  
Low Birth Weight ◽  
Regression Model ◽  
Bayesian Estimation ◽  
Logistic Regression Model ◽  
Estimation Method ◽  
Estimation Methods ◽  
Model Case

Abstract This study aims to compare the efficacy of logistic regression model for identifying the risk factors of low-birth-weight babies in Indonesia using the maximum likelihood estimation (MLE)and the Bayesian estimation methods. The data used in this study is secondary data derived from the 2017 Indonesian Demographic Health Survey with a total sample of 16,344 newborn babies. Selection of the best logistic regression model was based on the smaller Bayesian Schwartz Information Criterion (BIC) value. The logistic regression model with the Bayesian estimation method has a smaller BIC value than the MLE method. Twin births, baby girl, maternal age at risk, birth spacing that is too close, iron deficiency, low education, low economy, inadequate drinking water sources have provided a higher risk of low-birth-weight incidence.

scholarly journals Different Estimation Methods of the Stress-Strength Reliability Restricted Exponentiated Lomax Distribution

2021 ◽  
Vol 8 (3) ◽  
pp. 477-484
Author(s):  
Alaa M. Hamad ◽  
Bareq B. Salman
Keyword(s):  
Large Scale ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Traffic Modeling ◽  
Actuarial Science ◽  
Lomax Distribution ◽  
Shrinkage Methods ◽  
Probabilistic Distribution ◽  
Queue Theory

Lomax distribution, a large-scale probabilistic distribution used in industry, economics, actuarial science, queue theory, and Internet traffic modeling, is the most important distribution in reliability theory. In this paper estimating the reliability of Restricted exponentiated Lomax distribution in two cases, when one component X strength and Y stress R=P(Y<X), and when system content two component series strength, Y stress by using different estimation method. such as maximum likelihood, least square and shrinkage methods. A comparison between the outcomes results of the applied methods has been carried out based on mean square error (MSE) to investigate the best method and the obtained results have been displayed via MATLAB software package.

scholarly journals On Shrinkage Estimation for R(s, k) in Case of Exponentiated Pareto Distribution

2019 ◽  
Vol 32 (1) ◽  
pp. 152 ◽  
Author(s):  
Eman Ahmed Abdulateef ◽  
Abbas Najim Salman
Keyword(s):  
Pareto Distribution ◽  
Mean Squared Error ◽  
Multicomponent System ◽  
Estimation Method ◽  
Shrinkage Estimation ◽  
Scale Parameters ◽  
Squared Error ◽  
Simulation Based ◽  
Independent Distribution ◽  
Two Parameters

   This paper concerns with deriving and estimating the reliability of the multicomponent system in stress-strength model R(s,k), when the stress and strength are identical independent distribution (iid), follows two parameters Exponentiated Pareto Distribution(EPD) with the unknown shape and known scale parameters. Shrinkage estimation method including Maximum likelihood estimator (MLE), has been considered. Comparisons among the proposed estimators were made depending on simulation based on mean squared error (MSE) criteria.

On Reliability Estimation for the Exponential Distribution Based on Monte Carlo Simulation

2018 ◽  
pp. 428
Author(s):  
Abbas Najim Salman ◽  
Taha Anwar Taha
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Reliability Function ◽  
Reliability Estimation ◽  
Estimation Methods ◽  
Shrinkage Methods ◽  
Shrinkage Method ◽  
Two Parameters

        This Research deals with estimation the reliability function for two-parameters Exponential distribution, using different estimation methods ; Maximum likelihood, Median-First Order Statistics, Ridge Regression, Modified Thompson-Type Shrinkage and Single Stage Shrinkage methods. Comparisons among the estimators were made using Monte Carlo Simulation based on statistical indicter mean squared error (MSE) conclude that the shrinkage method perform better than the other methods

A simultaneous decision-making approach to model the demand for freight transportation

1991 ◽  
Vol 18 (3) ◽  
pp. 515-520 ◽  
Author(s):  
W. M. Abdelwahab ◽  
M. A. Sargious
Keyword(s):  
Maximum Likelihood ◽  
Discrete Choice ◽  
Choice Model ◽  
Mode Choice ◽  
Freight Transportation ◽  
Choice Models ◽  
Ordinary Least Squares ◽  
Discrete Choice Models ◽  
Estimation Methods ◽  
Complete Model

The application of discrete choice models (e.g., logit, probit) to study modal choice in passenger transportation has had a wide acceptance in the literature. However, little success had been reported on the application of these models to study the demand for freight transportation. This is mainly because in freight transportation a model that merely attempts to explain the choice of mode without taking into consideration other related factors, such as shipment size, is only one part of a complete model. Another type of models known as inventory-based models, which takes these factors into consideration, has been developed and applied with a greater success. However, the data requirement of these inventory models has hampered their applicability, especially in situations with limited data on goods movement. This paper presents a new approach to study the demand for intercity freight transportation. The model proposed in this paper utilizes the strength of discrete choice models (e.g., probit) in explaining the process of mode choice as one part of a complete model. The complete model is presented as a joint discrete/continuous choice model for the choices of mode and shipment size. The model is practical in that it requires the same amount and quality of data that would be required to develop a standard disaggregate mode choice model, and it can be estimated using simple two-stage estimation methods which utilizes standard probit maximum likelihood and ordinary least squares estimation techniques. Key words: disaggregate, freight transportation, maximum likelihood, mode, model, probit, shipment.

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