Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

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 "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

Modelling Significant Wave Height Data of North Sea: Rayleigh vs Weibull Distribution

2012 ◽  
Vol 157-158 ◽  
pp. 652-657
Author(s):  
Asma A. Shariff ◽  
M. Hadi Hafezi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Wave Height ◽  
Significant Wave Height ◽  
Likelihood Estimation ◽  
Rayleigh Distribution ◽  
Weibull Distributions ◽  
Significant Wave ◽  
Two Parameter

Significant wave height is generally defined as the mean height of the highest one third of the waves in the sample and is widely regarded as an approximate equivalent to the visually observed height. Some studies assumed that wave heights can be described in terms of Log-normal, Generalized Gamma and Beta distribution, while others proposed Rayleigh distributions. In this paper, we wish to compare Rayleigh distribution with those obtained using two-parameter Weibull distributions. Both Rayleigh and Weibull distributions are used to fit the empirical data obtained from the world's oceans Global Wave Statistics. The Rayleigh distribution parameter is estimated using Maximum Likelihood Estimation (MLE) while, for the two-parameter Weibull distribution, parameter values are obtained using Maximum Likelihood Estimation and Quantile Estimation (QE). A Chi-square goodness of fit test is then used to see how the fitted distributions compare with the empirical distribution. It is found that Weibull distributions are better fits than the Rayleigh distribution, and that the MLE estimation is the best in this respect.

Cubic Transmuted-G Family of Distributions and Its Properties

2018 ◽  
Vol 33 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criteria ◽  
Data Sets ◽  
New Family ◽  
Family Of Distributions

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

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