DanielAubin · DanielAubin · Jan 16, 2019 · Jan 16, 2019 · Nov 9, 2020 · Nov 9, 2020
diff --git a/MSMLLN/MSMLLN.py b/MSMLLN/MSMLLN.py
@@ -0,0 +1,22 @@
+# imports
+import numpy as np
+import matplotlib.pyplot as plt
+
+# plotting settings
+plt.style.use('seaborn')
+plt.rcParams['figure.figsize'] = (16, 8)
+
+np.random.seed(0)
+mu, sigma = 0, 1 # mean, standard deviation
+x = np.random.normal(mu, sigma, 1000)
+cum_sum = np.cumsum(x)
+sample_size = np.arange(1, len(x)+1)
+averges = np.divide(cum_sum, sample_size)
+
+plt.xlabel('Size of a sample', fontsize=16)
+plt.ylabel('Average', fontsize=16)
+plt.axhline(0, ls= '--', c='black', label='mean')
+plt.plot(sample_size, averges,
+         c='r', lw=5, alpha=0.6, label='sample average')
+plt.legend(loc="upper right", frameon=True, prop={'size': 14})
+plt.title('Law of Large Numbers', fontsize=20);
diff --git a/MSMLLN/MSMLLN.png → MSMLLN/MSMLLN_R.png b/MSMLLN/MSMLLN.png → MSMLLN/MSMLLN_R.png
diff --git a/MSMLLN/MSMLLN_py.png b/MSMLLN/MSMLLN_py.png
diff --git a/MSMLLN/Metainfo.txt b/MSMLLN/Metainfo.txt
@@ -3,9 +3,7 @@ Name of QuantLet : MSMLLN
 
 Published in : MSM
 
-Description : 'Plots the points showing law of large numbers. 
-As the sample size becomes larger, the sample mean converges to 
-the theoretical (true) mean of the distribution.'
+Description : 'Plots the points showing law of large numbers. As the sample size becomes larger, the sample mean converges to the theoretical (true) mean of the distribution.'
 
 Keywords : 
 - pdf
@@ -21,8 +19,8 @@ See also :
 - MSMpdfasymmetric
 - MSMasprob
 
-Author : Xiu Xu
+Author : Xiu Xu, Jacek Wiland
 
-Submitted : Thu, November 5 2015 by Chen Huang
+Submitted : December 15 2020 
 
 Example : Plot of points presenting law of large numbers.
diff --git a/MSMLLN/README.md b/MSMLLN/README.md
@@ -1,51 +1,42 @@
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
 
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MSMLLN** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MSMLLN
+```
+Name of QuantLet: MSMLLN
 
-Published in : MSM
+Published in: MSM
 
-Description : 'Plots the points showing law of large numbers. As the sample size becomes larger,
-the sample mean converges to the theoretical (true) mean of the distribution.'
+Description: Plots the points showing law of large numbers. As the sample size becomes larger, the sample mean converges to the theoretical (true) mean of the distribution.
 
-Keywords : pdf, normal, distribution, mean, plot, parameter, visualization, discrete
+Keywords: 
+- pdf
+- normal
+- distribution
+- mean
+- plot
+- parameter
+- visualization
+- discrete
 
-See also : MSMpdfasymmetric, MSMasprob
+See also: 
+- MSMpdfasymmetric
+- MSMasprob
 
-Author : Xiu Xu
+Author: Xiu Xu, Jacek Wiland
 
-Submitted : Thu, November 5 2015 by Chen Huang
+Submitted: December 15 2020
 
-Example : Plot of points presenting law of large numbers.
+Example: Plot of points presenting law of large numbers.
 
 ```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MSM/master/MSMLLN/MSMLLN_R.png" alt="Image" />
+</div>
 
-![Picture1](MSMLLN.png)
-
-
-### R Code:
-```r
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MSM/master/MSMLLN/MSMLLN_py.png" alt="Image" />
+</div>
 
-# clear history
-rm(list = ls(all = TRUE))
-graphics.off()
-
-n = 1000
-mu = 0
-sig = 1
-y = rnorm(n, mu, sig)
-x = matrix(0, nrow = n, ncol = 1)
-
-for (i in 1:n) {
-    x[i] = mean(y[1:i])
-}
-
-# Plot
-plot(x, col = "red3", type = "p", pch = 20, lwd = 2.5, ylab = "", xlab = "")
-abline(h = 0, col = "blue", pch = 20, lwd = 3.5)
-
-```
diff --git a/MSM_LIL/README.md b/MSM_LIL/README.md
@@ -1,74 +1,31 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MSM_LIL** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MSM_LIL
-
-Published in : MSM
-
-Description : 'Plots the average of n Bernoulli trials (each taking a value of +/- 1, with
-probability 0.5) to show the law of large numbers and the law of the iterated logarithm. Plots of
-sample mean (red), its asymptotic standard deviation (dark-green) and its bound given by law of
-iterated logarithm (blue).'
-
-Keywords : bernoulli, random, random-number-generation, simulation, plot
-
-Author : Chen Huang
-
-Author [New] : Ya Qian
-
-Submitted : Fri, October 16 2015 by Shi Chen
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
 
 ```
+Name of QuantLet: MSM_LIL
 
-![Picture1](MSM_LIL.png)
-
+Published in: MSM
 
-### R Code:
-```r
+Description: Plots the average of n Bernoulli trials (each taking a
 
-## clear history
-rm(list = ls(all = TRUE))
-graphics.off()
+Keywords: 
+- bernoulli
+- random
+- random-number-generation
+- simulation
+- plot
 
-## Initialize 
-y  = 0
-m  = 0
-N1 = 0
-N2 = 0
+Author: Chen Huang
 
-for (n in 1:1e+04) {
-    ## Simulate the paths of Bernoulli Distribution
-    y  = c(y, (1 + (-1 - 1) * (runif(1) < 0.5)))  
-    ## Calculate the sample mean
-    m  = c(m, mean(y[-1]))
-    ## Calculate the asymptotic standard deviation
-    N1 = c(N1, sqrt(1/n))
-    ## Calculate the bounds of the sample mean
-    N2 = c(N2, sqrt(2 * log(log(n))/n))
-}
+Author [New]: Ya Qian
 
-## Remove the initial zeros of each vector
-m  = m[-1]
-N1 = N1[-1]
-N2 = N2[-1]
-
-## Plot the sample mean 
-par(cex.lab = 1.5, cex.axis = 1.5, cex.main = 1.5, pch = 20)
-plot(m, ylim = c(-0.2, 0.2), type = "p", col = "red", main = "Law 
-     of the Iterated Logarithm", xlab = "Sample Size", ylab = 
-     "Deviation from Mean", cex = 0.5, bty = "n")
-legend(5000, 0.2, c("sqrt(1/n)", "sqrt(2 * log(log(n)) / n)"), 
-       lty = c(1, 1), col = c("dark green", "blue"), box.col = 
-       "white", pt.cex = 1.5 )
-
-## Add the asymptotic standard deviation and bounds
-lines(N1,  lty = 1, lwd = 2, col = "dark green")
-lines(-N1, lty = 1, lwd = 2, col = "dark green")
-lines(N2,  lty = 1, lwd = 2, col = "blue")
-lines(-N2, lty = 1, lwd = 2, col = "blue")
+Submitted: Fri, October 16 2015 by Shi Chen
 
 ```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MSM/master/MSM_LIL/MSM_LIL.png" alt="Image" />
+</div>
+
diff --git a/MSM_VaRandES/Metainfo.txt b/MSM_VaRandES/Metainfo.txt
@@ -13,7 +13,7 @@ Keywords :
 - cdf
 - plot
 
-Author : Chen Huang
+Author : Chen Huang, Fulvio Raddi
 
 Author [New] : Torsten Becker, Viktor Sandor
 

diff --git a/MSM_VaRandES/README.md b/MSM_VaRandES/README.md
@@ -1,73 +1,32 @@
-
-[<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/banner.png" width="888" alt="Visit QuantNet">](http://quantlet.de/)
-
-## [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **MSM_VaRandES** [<img src="https://github.com/QuantLet/Styleguide-and-FAQ/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/)
-
-```yaml
-
-Name of QuantLet : MSM_VaRandES
-
-Published in : MSM
-
-Description : 'Plots Value at Risk and Expected Shortfall in one figure and shows the relationship
-between VaR and ES.'
-
-Keywords : VaR, expected shortfall, lognormal, pdf, cdf, plot
-
-Author : Chen Huang
-
-Author [New] : Torsten Becker, Viktor Sandor
-
-Submitted : Thu, November 5 2015 by Chen Huang
+<div style="margin: 0; padding: 0; text-align: center; border: none;">
+<a href="https://quantlet.com" target="_blank" style="text-decoration: none; border: none;">
+<img src="https://github.com/StefanGam/test-repo/blob/main/quantlet_design.png?raw=true" alt="Header Image" width="100%" style="margin: 0; padding: 0; display: block; border: none;" />
+</a>
+</div>
 
 ```
+Name of QuantLet: MSM_VaRandES
 
-![Picture1](MSM_VaRandES.png)
-
-
-### R Code:
-```r
-
-# clear all variables
-rm(list = ls(all = TRUE))
-graphics.off()
+Published in: MSM
 
-dlognormalLoss = function(x) {
-  dlnorm(x, 0.5, 0.3)  # the density function
-}
+Description: Plots Value at Risk and Expected Shortfall in one figure and shows the relationship between VaR and ES.
 
-plognormalLoss = function(x) {
-  plnorm(x, 0.5, 0.3)  # the distribution function 
-}
+Keywords: 
+- VaR
+- expected shortfall
+- lognormal
+- pdf
+- cdf
+- plot
 
-curve(plognormalLoss, 0, 4, xlab = "Loss", ylab = "", lwd = 2)
-curve(dlognormalLoss, 0, 4, col = " black", lty = 2, lwd = 2, add = TRUE)
+Author: Chen Huang, Fulvio Raddi
 
-# Fill in the part beyond VaR with shadow
-x = seq(2.42, 4, length = 100)
-y = dlognormalLoss(x)
-x = c(2.42, x)
-y = c(dlognormalLoss(4), y)
-polygon(x, y, col = "grey", border = "grey")
-text(3.5, 0.2, expression(P(S > VaR[alpha]) == alpha))
-arrows(3, 0.2, 2.7, 0.05, lwd = 2)
+Author [New]: Torsten Becker, Viktor Sandor
 
-mtext(expression(VaR[alpha]), side = 1, at = 2.42)
-
-# Mark the Expected shortfall
-x = seq(2.42, 4, length = 100)
-y = plognormalLoss(x)
-x = c(0, x, 0)
-y = c(0.9, y, plognormalLoss(4))
-polygon(x, y, density = 20, col = "grey", border = "black", angle = 45)
-text(0.3, 0.93, expression(1 - alpha == 0.9))
-text(1.6, 0.95, expression(alpha * ES[alpha](X)))
-curve(plognormalLoss, 0, 4, lwd = 2, add = TRUE)
-curve(dlognormalLoss, 0, 4, col = "black", lty = 2, lwd = 2, add = TRUE)
-
-segments(2.42, -0.25, 2.42, 0.9)
-segments(-0.4, 0.9, 2.42, 0.9)
-
-legend(x = 2.5, y = 0.5, c("PDF", "CDF"), lty = c(2, 1)) 
+Submitted: Thu, November 5 2015 by Chen Huang
 
 ```
+<div align="center">
+<img src="https://raw.githubusercontent.com/QuantLet/MSM/master/MSM_VaRandES/MSM_VaRandES.png" alt="Image" />
+</div>
+
diff --git a/MSM_VaRandES/VaRandES.ipynb b/MSM_VaRandES/VaRandES.ipynb
diff --git a/MSMasprob/MSMasprob.py b/MSMasprob/MSMasprob.py
@@ -0,0 +1,27 @@
+# imports
+import numpy as np
+import matplotlib.pyplot as plt
+
+# plotting settings
+plt.style.use('seaborn')
+plt.rcParams['figure.figsize'] = (16, 8)
+
+# parameters
+n = 1000
+k = np.floor(np.log(n)/np.log(2)) - 1
+x = np.zeros([n, 10])
+x[0] = 1
+z = np.array([0.5, 0.2, 0.4, 0.6, 0.8])
+
+for s in range(2, len(z)+1):
+    for i in range(1, int(k+1)):
+        for j in range(0, 2**i + 1):
+            t = 2**i + j
+            x[t, 1] = (j * 2**(-i) <= 0.5) & (0.5 < (j + 1) * 2**(-i))
+            x[t, s] = (j * 2**(-i) <= z[s-1]) & (z[s-1] < (j + 1) * 2**(-i))
+            x = x * 1
+
+# Plot the time series
+plt.plot(x[1:400, 1], 'o', c = 'b', ms=5)
+plt.plot(x[1:400, 2], 'o', c = 'g', ms=5)
+plt.plot(x[1:400, 5], 'o', c = 'r', ms=5);
diff --git a/MSMasprob/MSMasprob.png → MSMasprob/MSMasprob_R.png b/MSMasprob/MSMasprob.png → MSMasprob/MSMasprob_R.png
diff --git a/MSMasprob/MSMasprob_py.png b/MSMasprob/MSMasprob_py.png
diff --git a/MSMasprob/Metainfo.txt b/MSMasprob/Metainfo.txt
@@ -3,10 +3,7 @@ Name of QuantLet : MSMasprob
 
 Published in : MSM
 
-Description : 'Displays an example of which meets the convergence in 
-mean square but not convergence in almost sure series of the example. 
-We select n = 400 and plot three cases: the initial value of 
-Z = 0.5 (blue), 0.2 (green), and 0.8 (dark red).'
+Description : 'Displays an example of which meets the convergence in mean square but not convergence in almost sure series of the example. We select n = 400 and plot three cases: the initial value of Z = 0.5 (blue), 0.2 (green), and 0.8 (dark red).'
 
 Keywords : 
 - random-number-generation
@@ -21,9 +18,8 @@ See also :
 - MSMpdfasymmetric
 - SFSmsr1
 
-Author : Xiu Xu
+Author: Xiu Xu, Jacek Wiland
 
-Submitted : Thu, November 5 2015 by Chen Huang
+Submitted :  December 15 2020
 
-Example : 'Plot of the series of a random variable satisfying convergence 
-in mean square but not convergence in almost sure.'
+Example : 'Plot of the series of a random variable satisfying convergence in mean square but not convergence in almost sure.'
-Original file line number
+Diff line change
@@ Expand Up / @@ -13,7 +13,7 @@ Keywords : @@
     - cdf
     - plot
-    Author : Chen Huang
+    Author : Chen Huang, Fulvio Raddi
     Author [New] : Torsten Becker, Viktor Sandor
@@ Expand Down @@