scholarly journals Intercomparison of estimators of extreme value family of distributions for rainfall frequency analysis

MAUSAM ◽  
2022 ◽  
Vol 73 (1) ◽  
pp. 59-70
Author(s):  
N. VIVEKANANDAN
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Likelihood Method ◽  
Extreme Value Analysis ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Value Analysis ◽  
Family Of Distributions

Estimation of rainfall for a given return period is of utmost importance for planning and design of minor and major hydraulic structures. This can be achieved through Extreme Value Analysis (EVA) of rainfall by fitting Extreme Value family of Distributions (EVD) such as Generalized Extreme Value, Extreme Value Type-1, Extreme Value Type-2 and Generalized Pareto to the series of observed Annual 1-Day Maximum Rainfall (AMR) data. Based on the intended applications and the variate under consideration, Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of probability distributions. The adequacy of fitting EVD to the AMR series was evaluated by quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic test (viz., D-index) tests and qualitative assessment by the fitted curves of the estimated rainfall. The paper presents a study on intercomparison of EVD (using MoM, MLM and LMO) adopted in EVA of rainfall with illustrative example and the results obtained thereof. 

scholarly journals Comparison of Generalized Extreme Value, Log Normal and Weibull Distributions for Assessment of Low-Flow

2021 ◽  
Vol 11 ◽  
pp. 34-41
Author(s):  
N. Vivekanandan
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Probability Distributions ◽  
Water Quality Management ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Low Flow ◽  
Likelihood Method ◽  
Generalized Extreme Value ◽  
Log Normal

Assessment of low-flow is an important aspect for water quality management, reservoir storage design, determining minimum release policy and safe surface water withdrawals. For which, the annual minimum d-day average flow is generally adopted procedure for characterizing the low-flow in a stream, which can be obtained by averaging the flow using moving average method for ‘d’ consecutive days viz., 7-, 10-, 14- and 30- days. This paper presents a study on comparison of three probability distributions such as Generalized Extreme Value, 2-parameter Log Normal (LN2) and Weibull adopted in estimation of low-flow for river Cauvery at Kollegal gauging site. The parameters are determined by three methods viz., method of moments, maximum likelihood method and L-Moments (LMO), and are used for estimation of low-flow. The adequacy of fitting probability distributions adopted in low-flow frequency analysis is evaluated by quantitative assessment through Goodness-of-Fit (viz., Chi-Square and Kolmogorov-Smirnov) and diagnostic (viz., correlation coefficient and root mean squared error) tests, and qualitative assessment using the fitted curves of the estimated low-flow. The results of quantitative and qualitative assessments indicate that LN2 (LMO) is better suited amongst three distributions adopted in estimation of 7-, 10-, 14- and 30- day low-flows for river Cauvery at Kollegal site.

Plotting positions for fitting distributions and extreme value analysis

2013 ◽  
Vol 40 (2) ◽  
pp. 130-139 ◽  
Author(s):  
M. Fuglem ◽  
G. Parr ◽  
I.J. Jordaan
Keyword(s):  
Probability Distributions ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Random Data ◽  
Value Analysis ◽  
Correct Method ◽  
Simulation Techniques ◽  
Probability Paper ◽  
Distribution Parameters ◽  
The Impact

Random data are often examined on plotting paper to determine appropriate probability distributions and distribution parameters for extreme-value analyses and other applications. Engineers are not always aware of criteria that have been developed and published for selecting the type of probability paper, nor of the impact that the selection can have on results. Some of the advice available in the literature is inaccurate, so it is important that the basis for using the correct method be clearly demonstrated. In the present paper, it is confirmed using straightforward simulation techniques that use of plotting position methods specific to the distribution being considered is appropriate and that use of other plotting position methods can give inaccurate results.

Modeling European hot spells using extreme value analysis

2014 ◽  
Vol 58 (3) ◽  
pp. 193-207 ◽  
Author(s):  
C Photiadou ◽  
MR Jones ◽  
D Keellings ◽  
CF Dewes
Keyword(s):  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Hot Spells

scholarly journals Threshold selection in univariate extreme value analysis

Extremes ◽  
2021 ◽  
Author(s):  
Laura Fee Schneider ◽  
Andrea Krajina ◽  
Tatyana Krivobokova
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Hill Estimator ◽  
Small Samples ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Wide Range ◽  
Asymptotic Mean Squared Error ◽  
The Hill

AbstractThreshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

Sign in / Sign up

Export Citation Format

Share Document