Bias correction for the maximum likelihood estimates in the two-parameter Weibull distribution

1999 ◽  
Vol 6 (1) ◽  
pp. 66-68 ◽  
Author(s):  
H. Hirose
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Bias Correction ◽  
Maximum Likelihood Estimates ◽  
Two Parameter

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

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 Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

2021 ◽  
Vol 50 (5) ◽  
pp. 38-51
Author(s):  
Mohammad Kazemi ◽  
Mina Azizpoor
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Unknown Parameters ◽  
Bayes Estimates ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Distribution Parameters ◽  
Highest Posterior Density

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

Estimation of Weibull Parameters Using Fractional Moments

1984 ◽  
Vol 33 (3-4) ◽  
pp. 179-186 ◽  
Author(s):  
S.P. Mukherjee ◽  
B.C. Sasmal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Relative Efficiency ◽  
Maximum Likelihood Estimators ◽  
Weibull Parameters ◽  
Moment Estimators ◽  
Fractional Moments ◽  
Distribution Moment ◽  
The Moment ◽  
Two Parameter

For a two-parameter Weibull distribution, moment estimators of the parameters have been developed by choosing orders of two moments (allowing fractions) so that the overall relative efficiency of the moment estimators compared with the maximum likelihood estimators is maximized . Some calculations in support of the superiority of fractional moments over integer moments in this connection have also been presented.

scholarly journals Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

2021 ◽  
Author(s):  
Xuechen Liu ◽  
Muhammad Arslan ◽  
Majid Khan ◽  
Syed Masroor Anwar ◽  
Zahid Rasheed
Keyword(s):  
Maximum Likelihood ◽  
Power Function ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Time Model ◽  
Data Set ◽  
Bayes Estimates ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Two Parameter

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

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