Call number:
9783030863906 (e-book)
Description / Table of Contents:
This book is of paramount importance in the fields of engineering and applied sciences, given that through the values obtained by these procedures, many structures, like spillways of dams and highway culverts, are designed and constructed.
The main aim of this book is to provide procedures for implementing many probability distribution functions, all of them based on using a standard and a common computational application known as Excel, which is available to any personal computer user. The computer procedures are given in enough detail, so readers can develop their own Excel worksheets.
All the probability distribution functions in the book have schemes to estimate its parameters, quantiles, and confidence limits through the methods of moments and maximum likelihood.
Type of Medium:
12
Pages:
1 Online-Ressource (XVII, 410 Seiten)
,
Illustrationen
ISBN:
9783030863906
,
978-3-030-86390-6
ISSN:
2730-6674
,
2730-6682
Series Statement:
Earth and environmental sciences library
URL:
https://doi.org/10.1007/978-3-030-86390-6
Language:
English
Note:
Contents
1 Introduction
1.1 Introduction
1.2 Brief History of Natural Extreme Events
1.3 Motivation and Goals
1.4 Chapter Outline
2 Basic Notions of Probability and Statistics for Natural Extreme Events Frequency Analyses
2.1 Introduction
2.2 Chapter Objectives
2.3 Basic Notions of Theory of Probability
2.3.1 Definition of Probability
2.3.2 Random Variables
2.3.3 Probability Distribution Functions
2.3.4 Probability Density Functions
2.3.5 Non-exceedance and Exceedance Probabilities
2.3.6 Return Period
2.4 Basic Notions of Statistics
2.4.1 Moments of a Distribution
2.4.2 Measures of Central Tendency
2.4.3 Measures of Dispersion
2.4.4 Measures of Symmetry
2.4.5 Measures of Peakedness
2.4.6 Descriptive Statistics
2.5 Methods for the Estimation of Parameters of Probability Distribution Functions
2.5.1 The Method of Moments (MOM)
2.5.2 The Method of Maximum Likelihood (ML)
2.5.3 The Method of Probability Weighted Moments (PWM)
2.6 Quantile Estimation and Frequency Factor
2.7 Plotting Position Formulas
2.8 Confidence Limits
2.9 Standard Errors of Estimates
2.9.1 MOM Method
2.9.2 ML Method
2.9.3 PWM Method
2.10 Plotting the Extreme Value Data and Models
2.10.1 Normal Probability Paper
2.10.2 Gumbel’s Probability Paper
2.11 Goodness of Fit Tests
2.11.1 The Standard Error of Fit
2.11.2 The Mean Absolute Relative Deviation
2.11.3 The Akaike’s Information Criterion
2.12 Outliers Tests
2.12.1 The Grubbs and Beck Test
2.13 Test for Independence and Stationarity
2.14 Test for Homogeneity and Stationarity
3 Normal Distribution
3.1 Introduction
3.2 Chapter Objectives
3.3 Probability Distribution and Density Functions
3.4 Estimation of Parameters
3.4.1 MOM Method
3.4.2 ML Method
3.5 Estimation of Quantiles for the NOR Distribution
3.5.1 Examples of Estimation of MOM and ML Quantiles for the NOR Distribution
3.6 Goodness of Fit Test
3.6.1 Examples of Application of the SEF and MARD to the MOM-ML Estimators of the Parameters of the NOR Distribution
3.7 Estimation of the Confidence Limits for the NOR Distribution
3.8 Estimation of the Standard Errors for the NOR Distribution
3.8.1 MOM Method
3.8.2 ML Method
3.9 Examples of Application for the NOR Distribution Using Excel® Spreadsheets
3.9.1 Flood Frequency Analysis
3.9.2 Rainfall Frequency Analysis
3.9.3 Wave Height Frequency Analysis
3.9.4 Maximum Annual Wind Speed Frequency Analysis
4 Two-Parameters Log-Normal Distribution
4.1 Introduction
4.2 Chapter Objectives
4.3 Probability Distribution and Density Functions
4.4 Estimation of the Parameters
4.4.1 MOM Method
4.4.2 ML Method
4.5 Estimation of Quantiles for the LN2 Distribution
4.5.1 Examples of Estimation of MOM and ML Quantiles for the LN2 Distribution
4.6 Goodness of Fit Test
4.6.1 Examples of Application of the SEF and MARD to the MOM and ML Estimators of the Parameters of the LN2 Distribution
4.7 Estimation of the Confidence Limits for the LN2 Distribution
4.8 Estimation of the Standard Errors for the LN2 Distribution
4.8.1 MOM Method
4.8.2 ML Method
4.9 Examples of Application for the LN2 Distribution Using Excel® Spreadsheets
4.9.1 Flood Frequency Analysis
4.9.2 Rainfall Frequency Analysis
4.9.3 Maximum Significant Wave Height Frequency Analysis
4.9.4 Annual Maximum Wind Speed Frequency Analysis
5 Three-Parameters Log-Normal Distribution
5.1 Introduction
5.2 Chapter Objectives
5.3 Probability Distribution and Density Functions
5.4 Estimation of the Parameters
5.4.1 MOM Method
5.4.2 ML Method
5.5 Estimation of Quantiles for the LN3 Distribution
5.5.1 Examples of Estimation of MOM Quantiles for the LN3 Distribution
5.6 Goodness of Fit Test
5.6.1 Examples of Application of the SEF and MARD to the MOM and ML Estimators of the Parameters of the LN3 Distribution
5.7 Estimation of the Confidence Limits for the LN3 Distribution
5.8 Estimation of the Standard Errors for the LN3 Distribution
5.8.1 MOM Method
5.8.2 ML Method
5.9 Examples of Application for the LN3 Distribution Using Excel® Spreadsheets
5.9.1 Flood Frequency Analysis
5.9.2 Rainfall Frequency Analysis
5.9.3 Maximum Significant Wave Height Frequency Analysis
5.9.4 Annual Maximum Wind Speed Frequency Analysis
6 Gamma Distribution
6.1 Introduction
6.2 Chapter Objectives
6.3 Probability Distribution and Density Functions
6.4 Estimation of the Parameters
6.4.1 MOM Method
6.4.2 ML Method
6.5 Estimation of Quantiles for the GAM Distribution
6.5.1 Examples of Estimation of MOM and ML Quantiles for the GAM Distribution
6.6 Goodness of Fit Test
6.6.1 Examples of Application of the SEF and MARD to the MOM and ML Estimators of the Parameters of the GAM Distribution
6.7 Estimation of Confidence Limits for the GAM Distribution
6.8 Estimation of Standard Errors for the GAM Distribution
6.8.1 MOM Method
6.8.2 ML Method
6.9 Examples of Application for the GAM Distribution Using Excel ® Spreadsheets
6.9.1 Flood Frequency Analysis
6.9.2 Rainfall Frequency Analysis
6.9.3 Maximum Significant Wave Height Frequency Analysis
6.9.4 Annual Maximum Wind Speed Frequency Analysis
7 Pearson Type III Distribution
7.1 Introduction
7.2 Chapter Objectives
7.3 Probability Distribution and Density Functions
7.4 Estimation of the Parameters
7.4.1 MOM Method
7.4.2 ML Method
7.5 Estimation of Quantiles for the PIII Distribution
7.5.1 Examples of Estimation of MOM and ML Quantiles for the PIII Distribution
7.6 Goodness of Fit Test
7.6.1 Examples of Application of the SEF and MARD to the MOM and ML Estimators of the Parameters of the PIII Distribution
7.7 Estimation of Confidence Limits for the PIII Distribution
7.8 Estimation of Standard Errors for the PIII Distribution
7.8.1 MOM Method
7.8.2 ML Method
7.9 Examples of Application for the PIII Distribution Using Excel® Spreadsheets
7.9.1 Flood Frequency Analysis
7.9.2 Rainfall Frequency Analysis
7.9.3 Maximum Significant Wave Height Frequency Analysis
7.9.4 Annual Maximum Wind Speed Frequency Analysis
8 Log-Pearson Type III Distribution
8.1 Introduction
8.2 Chapter Objectives
8.3 Probability Distribution and Density Functions
8.4 Estimation of the Parameters
8.4.1 MOM Method
8.4.2 ML Method
8.5 Estimation of Quantiles for the LPIII Distribution
8.5.1 Estimation of MOM1, MOM2 and ML Quantiles for the LPIII Distribution
8.5.2 Estimation of WRC Quantiles for the LPIII Distribution
8.5.3 Examples of Estimation of MOM1, MOM2, WRC and ML Quantiles for the LPIII Distribution
8.6 Goodness of Fit Test
8.6.1 Examples of Application of the SEF and MARD to the MOM1, WRC and ML Estimators of the Parameters of the LPIII Distribution
8.7 Estimation of Confidence Limits for the LPIII Distribution
8.7.1 Estimation of Confidence Limits for the LPIII Distribution for MOM1, MOM2, and ML Methods
8.7.2 Estimation of Confidence Limits for the LPIII Distribution for WRC Method
8.8 Estimation of Standard Errors for the LPIII Distribution
8.8.1 MOM Method
8.8.2 ML Method
8.9 Examples of Application for the LPIII Distribution Using Excel® Spreadsheets
8.9.1 Flood Frequency Analysis
8.9.2 Rainfall Frequency Analysis
8.9.3 Maximum Significant Wave Height Frequency Analysis
8.9.4 Annual Maximum Wind Speed Frequency Analysis
9 Extreme Value Type I Distribution
9.1 Introduction
9.2 Chapter Objectives
9.3 Probability Distribution and Density Functions
9.4 Estimation of the Parameters
9.4.1 MOM Method
9.4.2 ML Method
9.4.3 PWM Method
9.5 Estimation of Quantiles for the EVI Distribution
9.5.1 Examples of Estimation of MOM, ML and PWM Quantiles for the EVI Distribution
9.6 Goodness of Fit Test
9.6.1 Examples of Application of the SEF and MARD to the MOM, ML and PWM Estimators of the Parameters of the EVI Distribution
9.7 Estimation of Confidence Limits for the EVI Distribution
9.8 Estimation of Standard Errors for the EVI Distribution
9.8.1 MOM Method
9.8.2 ML Method
9.8.3 PWM Method
9.9 Examples of Application for the EVI Distribution Using Excel® Spreadsheets
9.9.1 Flood Frequency Analysis
9.9.2 Rainfall Frequency Analysis
9.9.3 Maximum Significant Wave Height Frequency Analysis
9.9.4 Annual Maximum Wind Speed Frequency Analy
Permalink
