Reliability Analysis of the Hydro-System of Excavator SchRs 800 Using Weibull Distribution

2015 ◽  
Vol 806 ◽  
pp. 173-180 ◽  
Author(s):  
Predrag Dašić ◽  
Milutin Živković ◽  
Marina Karić
Keyword(s):  
Weibull Distribution ◽  
Reliability Analysis ◽  
Goodness Of Fit ◽  
Weibull Model ◽  
Reliability Model ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Von Mises

In this paper is given the use Weibull distribution (WD) as theoretical reliability model for analysis of the hydro-system of excavator SchRs 800, which is accepted on the basis of Pearson (χ2), Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) goodness-of-fit tests. The time of work without failure of the hydro-system of excavator SchRs 800 for accepted Weibull model of reliability for probability of 50 % is T50%=0.3417⋅103[h], for probability of 80 % is T80%=0.1884⋅103[h] and for probability of 90% is T90%=0.127⋅103[h].

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

2017 ◽  
Vol 28 (2) ◽  
pp. 30-42 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Sorana D. Bolboacă
Keyword(s):  
Experimental Data ◽  
Goodness Of Fit ◽  
Error Function ◽  
Shannon’S Entropy ◽  
Goodness Of Fit Test ◽  
Shannon's Entropy ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

AbstractStatistical analysis starts with the assessment of the distribution of experimental data. Different statistics are used to test the null hypothesis (H0) stated as Data follow a certain/specified distribution. In this paper, a new test based on Shannon’s entropy (called Shannon’s entropy statistic, H1) is introduced as goodness-of-fit test. The performance of the Shannon’s entropy statistic was tested on simulated and/or experimental data with uniform and respectively four continuous distributions (as error function, generalized extreme value, lognormal, and normal). The experimental data used in the assessment were properties or activities of active chemical compounds. Five known goodness-of-fit tests namely Anderson-Darling, Kolmogorov-Smirnov, Cramér-von Mises, Kuiper V, and Watson U2 were used to accompany and assess the performances of H1.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Masoumeh Akbari
Keyword(s):  
Order Statistics ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Probability Function ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Definition Of ◽  
Von Mises ◽  
First Moment

In this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions xn,0<x<1,n≥1. Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.

scholarly journals Goodness of fit tests for Rayleigh distribution based on Phi-divergence

2017 ◽  
Vol 40 (2) ◽  
pp. 279-290 ◽  
Author(s):  
Mahdi Mahdizadeh ◽  
Ehsan Zamanzade
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Data Set ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

In this paper, we develop some goodness of fit tests for Rayleigh distribution based on Phi-divergence. Using Monte Carlo simulation, we compare the power of the proposed tests with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer von-Mises tests. The results indicate that the proposed tests perform well as compared with their competing tests in the literature. Finally, the proposed procedures are illustrated via a real data set.

scholarly journals Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands in Poland

Forests ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 412 ◽  
Author(s):  
Piotr Pogoda ◽  
Wojciech Ochał ◽  
Stanisław Orzeł
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Alnus Glutinosa ◽  
Weibull Model ◽  
Diameter Distribution ◽  
Stand Age ◽  
Weibull Function ◽  
Black Alder ◽  
Kolmogorov Smirnov ◽  
Non Parametric

We present diameter distribution models for black alder (Alnus glutinosa (L.) Gaertn.) derived from diameter measurements made at breast height in 844 circular sample plots set in 163 managed stands located in south-eastern Poland. A total of 22,530 trees were measured. Stand age ranged from six to 89 years. The model formulation was based on the two-parameter Weibull function and a non-parametric percentile-based method. Weibull function parameters were recovered from the first raw and second central moments estimated using the stand quadratic mean diameter. The same stand characteristic was used to predict values of 12 percentiles in the percentile-based method. The model performance was assessed using the k-fold cross-validation method. The goodness-of-fit statistics include the Kolmogorov–Smirnov statistic, mean error, root mean squared error, and two variants of the error index introduced by Reynolds. The percentile model developed, accurately predicted diameter distributions in 88.4% of black alder stands, as compared to 81.9% for the Weibull model (Kolmogorov–Smirnov test). Alternative statistical metrics assessing goodness-of-fit to empirical distributions suggested that the non-parametric percentile model was superior to the parametric Weibull model, especially in stands older than 20 years. In younger stands, the two models were accurate only in 57% of the cases, and did not differ significantly with respect to goodness-of-fit measures.

scholarly journals Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

2003 ◽  
Vol 33 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Vytaras Brazauskas ◽  
Robert Serfling
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Efficient Estimation ◽  
Small Samples ◽  
Robust Estimators ◽  
Trade Offs ◽  
Pareto Model ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

A new method for process control based on goodness of fit tests

2015 ◽  
Vol 32 (2) ◽  
pp. 132-143
Author(s):  
Mohammad Saleh Owlia ◽  
Mohammad Saber Fallah Nezhad ◽  
Mohesn Sheikh Sajadieh
Keyword(s):  
Process Control ◽  
Design Methodology ◽  
Goodness Of Fit ◽  
New Method ◽  
Content Type ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Shift Detection ◽  
The Subject ◽  
Smirnov Test

Purpose – The purpose of this paper is to propose a new method based on goodness of fit tests for shift detection problems. Design/methodology/approach – In this method, although the distribution of gathered data from the process is the subject of control, but any out-of-control signal could also be generalized to the overall state of the process including the parameters of the distribution. Findings – Results of simulation study denote that among goodness of fit tests, the χ2 test has a better performance than the Kolmogorov-Smirnov test in detecting shifts of process. Also comparison of proposed method with traditional methods denotes that, proposed method generally has smaller probabilities of first and second type errors. Originality/value – To the best of author’s knowledge, no attention has previously been paid to application of goodness of fit tests in process control.

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