scholarly journals Critical values of modified Kolmogorov-Smirnov goodness-of-fit tests for the extreme-value and two-parameter Weibull distributions.

1990 ◽  
Vol 39 (436) ◽  
pp. 45-49 ◽  
Author(s):  
Toshiyuki SHIMOKAWA
Keyword(s):  
Goodness Of Fit ◽  
Extreme Value ◽  
Critical Values ◽  
Weibull Distributions ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Two Parameter

scholarly journals Estimation of flood frequency using statistical method: Mahanadi River basin, India

2020 ◽  
Vol 3 (1) ◽  
pp. 189-207
Author(s):  
Sandeep Samantaray ◽  
Abinash Sahoo
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Central India ◽  
Extreme Value ◽  
Flood Frequency ◽  
Goodness Of Fit Test ◽  
Mahanadi River ◽  
Goodness Of Fit Tests ◽  
Study Results ◽  
Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

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.

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 Portfolio Tail Risk: A Multivariate Extreme Value Theory Approach

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1425
Author(s):  
Miloš Božović
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Value Theory ◽  
Extreme Value ◽  
Theory Approach ◽  
Risk Modeling ◽  
Tail Risk ◽  
Goodness Of Fit Tests ◽  
Level Of Significance

This paper develops a method for assessing portfolio tail risk based on extreme value theory. The technique applies separate estimations of univariate series and allows for closed-form expressions for Value at Risk and Expected Shortfall. Its forecasting ability is tested on a portfolio of U.S. stocks. The in-sample goodness-of-fit tests indicate that the proposed approach is better suited for portfolio risk modeling under extreme market movements than comparable multivariate parametric methods. Backtesting across multiple quantiles demonstrates that the model cannot be rejected at any reasonable level of significance, even when periods of stress are included. Numerical simulations corroborate the empirical results.

Embedded Distributions: Two Numerical Examples

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Asymptotic Theory ◽  
Extreme Value ◽  
Confidence Bands ◽  
Fibre Strength ◽  
Data Sets ◽  
Strength Data ◽  
Log Likelihood ◽  
Embedded Model ◽  
Two Parameter

This chapter illustrates use of (i) the score statistic and (ii) a goodness-of-fit statistic to test if an embedded model provides an adequate fit, in the latter case with critical values calculated by bootstrapping. Also illustrated is (iii) calculation of parameter confidence intervals and CDF confidence bands using both asymptotic theory and bootstrapping, and (iv) use of profile log-likelihood plots to display the form of the maximized log-likelihood and scatterplots for checking convergence to normality of estimated parameter distributions. Two different data sets are analysed. In the first, the generalized extreme value (GEVMin) distribution and its embedded model the simple extreme value (EVMin) are fitted to Kevlar-fibre breaking strength data. In the second sample, the four-parameter Burr XII distribution, its three-parameter embedded models, the GEVMin, Type II generalized logistic and Pareto and two-parameter embedded models, the EVMin and shifted exponential, are fitted to carbon-fibre strength data and compared.

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