Extreme values statistical analysis library

Library of functions for the statistical analysis of extreme values

This library provides many interesting tools for the analysis of extreme events.

1) Basic functions (density function, cumulative distribution function, inverse-cdf, random generator, parameter estimation) for many statistical distributions :

a) Generalized extreme value distribution

b) Gumbel distribution

c) Logistic distribution

d) Normal distribution

e) Uniform distribution

f) Exponential distribution (2 parameters)

g) Generalized logistic distribution

h) Generalized Pareto distribution

i) LogNormal distrubution (with 2 parameters)

j) LogNormal distribution (with 3-parameters)

k) Pearson 3 distribution

l) Log-Pearson 3 distribution

m) Gamma distribution

2) Annual maxima extraction tool from timeseries

3) Choosing the appropriate distribution

4) QQplots

5) Quantiles estimates with confidence interval

6) Akaike Information criterion and log-likelihood function

7) Finding the L-moments of a sample

8) Functions and an example for a Regional Frequency Analysis (RFA), when multiples samples are available

- Verification of homogeneity, stationarity and independance of the samples

- Calculate the regional L-moments

- Verification of the regional homogeniety

- Goodness-of-fit test for the RFA

- Compute the regional quantiles and the confidence interval

The Matlab Statistical Toolbox isn't necessary, except for the "example_xxx" scripts, where I use the "quantile.m" function. If not available, I recommend you download the "Quantiles" function by David Ferreira (https://www.mathworks.com/matlabcentral/fileexchange/70279-quantiles) and place it in your directory.

The RFA confidence interval function also requires the statistical toolbox.

The fitting of the parameters is based on the L-moment method from Hosking and Wallis (1997) :

Hosking, J., & Wallis, J. (1997). Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511529443

Your comments/suggestions are welcome!