Maximum likelihood estimation foe two parameter exponentials under type I censoring

1988 ◽  
Vol 17 (9) ◽  
pp. 2859-2879 ◽  
Author(s):  
Malay Ghosh ◽  
Lily Liorens Mantelle
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Type I ◽  
Type I Censoring ◽  
Two Parameter

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.

A statistical method for determining normal ranges from laboratory data including values below the minimum detectable value.

1979 ◽  
Vol 25 (12) ◽  
pp. 2011-2014 ◽  
Author(s):  
J Y Tsay ◽  
I W Chen ◽  
H R Maxon ◽  
L Heminger
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Method ◽  
Laboratory Data ◽  
Likelihood Estimation ◽  
Type I ◽  
Tolerance Limits ◽  
Normal Range ◽  
Normal Ranges

Abstract Determination of normal ranges from laboratory data containing undectable values is a frequently encountered problem in the radioimmunoassay of peptide hormones. In the past, such determinations usually have been based on the mid-point method or the one-end Winsorized method. A graphic method involving the use of probability paper has also been reported. We propose that the maximum-likelihood estimation is a more appropriate statistical method for the determination of normal range from this type of data (Type I censored data). With this method, the mean and standard deviation, and hence the tolerance limits, can be estimated. We used the maximum-likelihood estimation method to determine the normal range of serum thyrotropin values obtained from 93 healthy subjects, based on a log normal distribution. Although the serum thyrotropin content was undetectable in 14% of the subjects, a normal range could be calculated. Using tolerance limits for 95% coverage of the population with 90% confidence, we calculated the normal range of thyrotropin to be 0.51-5.75 milliunits/L, with a mean value of 1.71 milliunits/L, and predicted that 91.4% of undetectable serum thyrotropin values will fall within the normal range.

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