From 33f31bc8bd11c1edfc138579ea7bcf6f8443bfe4 Mon Sep 17 00:00:00 2001
From: Le Roux Erwan <erwan.le-roux@irstea.fr>
Date: Thu, 13 Dec 2018 15:35:44 +0100
Subject: [PATCH] [THESIS REPORT] add quantile plot
---
example.R | 35 -----------------------------------
thesis_report/gev_plot.py | 22 +++++++++++++++++++---
2 files changed, 19 insertions(+), 38 deletions(-)
delete mode 100644 example.R
diff --git a/example.R b/example.R
deleted file mode 100644
index 0083b6ea..00000000
--- a/example.R
+++ /dev/null
@@ -1,35 +0,0 @@
-library(SpatialExtremes)
-# Title : TODO
-# Objective : TODO
-# Created by: erwan
-# Created on: 27/11/18
-# define the coordinate of each location
-set.seed(42)
-n.site <- 30
-locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
-colnames(locations) <- c("lon", "lat")
-print(locations)
-##Simulate a max-stable process - with unit Frechet margins
-data <- rmaxstab(40, locations, cov.mod = "whitmat", nugget = 0, range = 3,
-smooth = 0.5)
-##Now define the spatial model for the GEV parameters
-param.loc <- -10 + 2 * locations[,2]
-param.scale <- 5 + 2 * locations[,1] + locations[,2]^2
-param.shape <- rep(0.2, n.site)
-##Transform the unit Frechet margins to GEV
-for (i in 1:n.site)
-data[,i] <- frech2gev(data[,i], param.loc[i], param.scale[i], param.shape[i])
-##Define a model for the GEV margins to be fitted
-##shape ~ 1 stands for the GEV shape parameter is constant
-##over the region
-loc.form <- loc ~ lat
-scale.form <- scale ~ lon + I(lat^2)
-shape.form <- shape ~ 1
-##Fit a max-stable process using the Schlather
-res = fitmaxstab(data, locations, "whitmat", loc.form, scale.form, shape.form)
-print(res['fitted.values'])
-## Model without any spatial structure for the GEV parameters
-## Be careful this could be *REALLY* time consuming
-# res = fitmaxstab(data, locations, "whitmat", fit.margin=TRUE)
-# print(res['fitted.values'])
-
diff --git a/thesis_report/gev_plot.py b/thesis_report/gev_plot.py
index d2d6b9e5..a5916cc0 100644
--- a/thesis_report/gev_plot.py
+++ b/thesis_report/gev_plot.py
@@ -28,7 +28,7 @@ def max_stable_plot():
lim = 10 ** (power_n)
x = np.linspace(0, lim, 100)
loc, scale, shape = 1, 1, 1
- for n in [10**i for i in range(power_n)]:
+ for n in [10 ** i for i in range(power_n)]:
label = 'n={}'.format(n)
y = np.array(r.pgev(x, loc, scale, shape))
y **= n
@@ -40,6 +40,22 @@ def max_stable_plot():
plt.show()
+def quantile_function_plot():
+ p = np.linspace(5e-1, 1e-5, 100)
+ loc, scale = 2, 1
+ shapes = [-1, 0, 1]
+ for shape in shapes:
+ label = '$\zeta= {} $'.format(shape)
+ funct = [r.qgev, r.qgpd][0]
+ y = funct(1 - p, loc, scale, shape)
+ plt.loglog(1/p, y, basex=10, label=label)
+ plt.legend()
+ plt.xlabel('$1/p$')
+ plt.ylabel('$q(1- p|\mu, \sigma, \zeta)$')
+ plt.show()
+
+
if __name__ == '__main__':
-# gev_plot()
- max_stable_plot()
+ # gev_plot()
+ # max_stable_plot()
+ quantile_function_plot()
\ No newline at end of file
--
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