scholarly journals Maximum logq Likelihood Estimation for Parameters of Weibull Distribution and Properties: Monte Carlo Simulation

2021 ◽  
Author(s):  
Mehmet Niyazi Cankaya ◽  
Roberto Vila
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Weibull Distribution ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
P Value ◽  
Test Statistic ◽  
Log Likelihood

Abstract The maximum logq likelihood estimation method is a generalization of the known maximum log likelihood method to overcome the problem for modeling non-identical observations ( inliers and outliers). The parameter $q$ is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function p(x; ʘ) = logq [f(x; ʘ)], we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers . The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by logq and its special form, log , likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of p(x; ʘ) and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of $q$ can be chosen by use of the mean squared error in simulation and the $p$ -value of Kolmogorov - Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of $q$ for real data sets.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

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.

ON THE PROPERTIES AND MLEs OF GENERALIZED ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION

2021 ◽  
Vol 4 (4) ◽  
pp. 155-165
Author(s):  
Aminu Suleiman Mohammed ◽  
Badamasi Abba ◽  
Abubakar G. Musa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Lifetime Data ◽  
Failure Rates ◽  
Simulation Experiments

For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics.  We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to provide a promising parameter estimates, and hence can be adopted in practice for estimating the parameters of the distribution. An application to real and simulated datasets indicated that the new model is superior to the fits than the other compared distributions

scholarly journals The Topp-Leone Weibull Distribution: Its Properties and Application

2021 ◽  
pp. 381-401
Author(s):  
Diamond O. Tuoyo ◽  
Festus C. Opone ◽  
N. Ekhosuehi
Keyword(s):  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Lifetime Data ◽  
Test Statistic ◽  
Data Set ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This paper presents a new generalization of the Topp-Leone distribution called the Topp-Leone Weibull Distribution (TLWD). Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method is adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions, to a real lifetime data set reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized log-likelihood, Akaike Information Criterion [AIC=2k-2 log⁡(L) ], Kolmogorov-Smirnov test statistic (K-S) and Anderson Darling test statistic (A*) and Crammer-Von Mises test statistic (W*).

scholarly journals A THIRD GENERATION TOMOGRAPHY SYSTEM WITH FIFTEEN DETECTORS SIMULATED BY MONTE CARLO METHOD

2019 ◽  
Vol 7 (2A) ◽  
Author(s):  
Alexandre Gimenez Alvarez ◽  
Alexandre França Velo ◽  
Vagner Fernandez ◽  
Samir L. Somessari ◽  
Francisco F. Sprenger ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Estimation Method ◽  
Pulse Height ◽  
Likelihood Estimation ◽  
Third Generation ◽  
Tomography System ◽  
Beam Geometry ◽  
Iterative Maximum Likelihood ◽  
Maximum Likelihood Estimation Method

This paper describes the Monte Carlo simulation, using MCNP4C, of a multichannel third generation tomography system containing a two radioactive sources 192I (316.5 – 468 KeV) and 137Cs (662 KeV), and a set of fifteen NaI(Tl) detectors, with dimensions of 1 inch diameter and  2 inches thick, in fan beam geometry, positioned diametrically opposite. Each detector moves 10 steps of 0,24o, totalizing 150 virtual detectors per projection, and then the system rotate 2 degrees. The Monte Carlo simulation was performed to evaluate the viability of this configuration. For this, a multiphase phantom containing polymethyl methacralate (PMMA ((r @ 1.19 g/cm3)), iron (r @ 7.874 g/cm3), aluminum (r @ 2.6989 g/cm3) and air (r @ 1.20479E-03 g/cm3) was simulated. The simulated number of histories was 1.1E+09 per projection and the tally used were the F8, which gives the pulse height of each detector. The data obtained by the simulation was used to reconstruct the simulated phantom using the statistical iterative Maximum Likelihood Estimation Method Technique (ML-EM) algorithm. Each detector provides a gamma spectrum of the sources, and a pulse height analyzer (PHA) of 10% on the 316.5 KeV and 662 KeV photopeaks was performed. This technique provides two reconstructed images of the simulated phantom. The reconstructed images provided high spatial resolution, and it is supposed that the temporal resolution (spending time for one complete revolution) is about 2.5 hours.

scholarly journals The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hisham M. Almongy ◽  
Ehab M. Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
E. H. Hafez ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Exponential Distribution ◽  
Estimation Method ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Mcmc Methods ◽  
Generalized Exponential Distribution ◽  
Censored Sample ◽  
Sample Maximum

This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type-II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice.

scholarly journals Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

2006 ◽  
Vol 3 (4) ◽  
pp. 1603-1627 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M. van Gelder ◽  
J. K. Vrijling ◽  
X. Chen
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Long Memory ◽  
Positive Relationship ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Large Data ◽  
Daily Streamflow ◽  
Maximum Likelihood Estimation Method

Abstract. The Lo's R/S tests (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the maximum likelihood estimation method implemented in S-Plus (S-MLE) are evaluated through intensive Mote Carlo simulations for detecting the existence of long-memory. It is shown that, it is difficult to find an appropriate lag q for Lo's test for different AR and ARFIMA processes, which makes the use of Lo's test very tricky. In general, the GPH test outperforms the Lo's test, but for cases where there is strong autocorrelations (e.g., AR(1) processes with φ=0.97 or even 0.99), the GPH test is totally useless, even for time series of large data size. Although S-MLE method does not provide a statistic test for the existence of long-memory, the estimates of d given by S-MLE seems to give a good indication of whether or not the long-memory is present. Data size has a significant impact on the power of all the three methods. Generally, the power of Lo's test and GPH test increases with the increase of data size, and the estimates of d with GPH test and S-MLE converge with the increase of data size. According to the results with the Lo's R/S test (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the S-MLE method, all daily flow series exhibit long-memory. The intensity of long-memory in daily streamflow processes has only a very weak positive relationship with the scale of watershed.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

Reliability Analysis for Masked Data under Type-II Generalized Progressively Hybrid Censored Scheme

2014 ◽  
Vol 687-691 ◽  
pp. 1198-1201
Author(s):  
Bin Liu ◽  
Yi Min Shi ◽  
Jing Cai ◽  
Mo Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Type Ii ◽  
Distribution Parameters ◽  
System Lifetime Data ◽  
Quasi Newton

The Type-II generalized progressively hybrid censored scheme with masked data is presented. Based on masked system lifetime data, using the expectation maximization algorithm and the Quasi-Newton method, we obtain the Maximum Likelihood Estimation (MLE) of the components distribution parameters in the Weibull case. Finally, Monte Carlo simulation is presented to illustrate the effect.

Gas Turbine Safety Improvement Through Risk Analysis

1988 ◽  
Vol 110 (2) ◽  
pp. 265-270 ◽  
Author(s):  
T. M. Crosby ◽  
G. L. Reinman
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Risk Analysis ◽  
Weibull Distribution ◽  
Gas Turbine ◽  
System Model ◽  
Weibull Analysis ◽  
System Safety ◽  
Weibull Plot ◽  
Safety Improvement

This paper is intended to provide the engineer with the information necessary to understand certain statistical methods that are used to improve system safety. It will provide an understanding of Weibull analysis, in that it describes when the Weibull distribution is appropriate, how to construct a Weibull plot, and how to use the parameters of the Weibull distribution to calculate risk. The paper will also provide the engineer with a comprehension of Monte Carlo simulation as it relates to quantifying safety risk. The basic components of Monte Carlo simulation are discussed as well as the formulation of a system model and its application in the gas turbine industry.

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