Confidence and Tolerance Bounds and a New Goodness-of-Fit Test for Two- Parameter Weibull or Extreme-Value Distributions (with Tables for Censored Samples of Size 3(1)25)

1971 ◽  
Author(s):  
Nancy R. Mann ◽  
Kenneth W. Fertig ◽  
Ernest M. Scheuer
Keyword(s):  
Goodness Of Fit ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Goodness Of Fit Test ◽  
Censored Samples ◽  
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.

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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