scholarly journals Inferences on A Normal Mean with an Auxiliary Variable

2021 ◽  
Vol 25 (2) ◽  
pp. 51-59
Author(s):  
Jianqi Yu ◽  
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Monte Carlo Simulations ◽  
Hypothesis Testing ◽  
Likelihood Estimation ◽  
Auxiliary Variable ◽  
Confidence Estimation ◽  
Normal Mean ◽  
The Mean

Inferential procedures for a normal mean with an auxiliary variable are developed. First, the maximum likelihood estimation of the mean and its distribution are derived. Second, an F statistic based on the maximum likelihood estimation is proposed, and the hypothesis testing and confidence estimation are outlined. Finally, to illustrate the advantage of using auxiliary variable, Monte Carlo simulations are performed. The results indicate that using auxiliary variable can improve the efficiency of inference.

Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables

2001 ◽  
Vol 9 (4) ◽  
pp. 325-346 ◽  
Author(s):  
Philip Paolino
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Monte Carlo Simulations ◽  
Interest Groups ◽  
Political Science ◽  
Beta Distribution ◽  
Likelihood Estimation ◽  
Dependent Variables ◽  
Key Aspects

Research in political science is often concerned with modeling dependent variables that are proportions. Proportions are relevant in a wide variety of substantive areas, including elections, the bureaucracy, and interest groups. Yet because most researchers rely upon an approach, OLS, that does not recognize key aspects of proportions, the conclusions we reach from normal models may not provide the best understanding of phenomena of interest in these areas. In this paper, I use Monte Carlo simulations to show that maximum likelihood estimation of these data using the beta distribution may provide more accurate and more precise results. I then present empirical analyses illustrating some of these differences.

Failure rate analysis of jaw crusher using Weibull model

2016 ◽  
Vol 231 (4) ◽  
pp. 760-772 ◽  
Author(s):  
RS Sinha ◽  
AK Mukhopadhyay
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Jaw Crusher ◽  
Two Parameter

The primary crusher is essential equipment employed for comminuting the mineral in processing plants. Any kind of failure of its components will accordingly hinder the performance of the plant. Therefore, to minimize sudden failures, analysis should be undertaken to improve performance and operational reliability of the crushers and its components. This paper considers the methods for analyzing failure rates of a jaw crusher and its critical components application of a two-parameter Weibull distribution in a mineral processing plant fitted using statistical tests such as goodness of fit and maximum likelihood estimation. Monte Carlo simulation, analysis of variance, and artificial neural network are also applied. Two-parameter Weibull distribution is found to be the best fit distribution using Kolmogorov–Smirnov test. Maximum likelihood estimation method is used to find out the shape and scale parameter of two-parameter Weibull distribution. Monte Carlo simulation generates 40 numbers of shape parameters, scale parameters, and time. Further, 40 numbers of Weibull distribution parameters are evaluated to examine the failure rate, significant difference, and regression coefficient using ANOVA. Artificial neural network with back-propagation algorithm is used to determine R2 and is compared with analysis of variance.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

scholarly journals Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

2020 ◽  
Vol 68 (6) ◽  
pp. 1896-1912
Author(s):  
Yijie Peng ◽  
Michael C. Fu ◽  
Bernd Heidergott ◽  
Henry Lam
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Modeling ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Data Driven ◽  
Simulation Based

A Simulation-Based Approach for Calibrating Stochastic Models

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