Added many thing, check the code Paul

Probas.py

@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 from random import random
-from math import floor, sqrt
+from math import floor, sqrt,factorial
 from statistics import mean, variance
 from matplotlib import pyplot as plt
 from pylab import *
@@ -185,55 +185,77 @@ def stats_NFDBP(R, N,t_i):
     T=[]
     Tk=[[] for _ in range(N)]
     Ti=[]
+    T_maths=[]
     #First iteration to use zip after
     sim=simulate_NFDBP(N)
-    Sum_T=sim["T"]
+    Sum_T=[0 for _ in range(N)]
     for i in range(R):
         sim = simulate_NFDBP(N)
         I.append(sim["i"])
+        for k in range(N):
+            T.append(0)
+            T=sim["T"]
         for n in range(N):
             H[n].append(sim["H"][n])
             Tk[n].append(sim["T"][n])
-        T=sim["T"]
         Ti.append(sim["T"])
-        for k in range(N):
-            Sum_T.append(0)
-            T.append(0)
         Sum_T=[x+y for x,y in zip(Sum_T,T)]
     Sum_T=[x/R for x in Sum_T] #Experimental [Ti=k]
     Sum_T=[x*100/(sum(Sum_T)) for x in Sum_T] #Pourcentage de la repartition des items 
-    print(Tk)
+    
     print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))
 
     for n in range(N):
         print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
     print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
-
+    #Loi math
+    for u in range(N):
+        u=u+2
+        T_maths.append(1/(factorial(u-1))-1/factorial(u))
+    E=0
+    sigma2=0
+    print("hep")
+    print(T_maths)
+    for p in range(len(T_maths)):
+        E=E+(p+1)*T_maths[p]
+        sigma2=((T_maths[p]-E)**2)/(len(T_maths)-1)
+    print("Mathematical values : Empiric mean T_{} : {} Variance {})".format(t_i, E, sqrt(sigma2)))
+    T_maths=[x*100 for x in T_maths]
 #Plotting
     fig = plt.figure()
     #T plot
     x =  np.arange(N)
     print(x)
-    ax = fig.add_subplot(121)
+    print(Sum_T)
+    ax = fig.add_subplot(221)
     ax.bar(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
-    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
+    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,20), yticks=np.linspace(0, 20, 2))
-    ax.set_ylabel('Items')
+    ax.set_ylabel('Items(n) in %')
     ax.set_xlabel('Boxes (1-{})'.format(N))
-    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
+    ax.set_title('Items percentage for each box and {} packages (Number of packages in each box)'.format(P))
     ax.legend(loc='upper left',title='Legend')
+
+    #Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
+    print(len(Tk[t_i]))
+    bx = fig.add_subplot(222)
+    bx.hist(Tk[t_i],bins=10, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
+    bx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,len(Tk[t_i])), yticks=np.linspace(0, 1, 1))
+    bx.set_ylabel('P(T{}=i)'.format(t_i))
+    bx.set_xlabel('Boxes i=(1-{}) in %'.format(N))
+    bx.set_title('T{} histogram for {} packages (Number of packages in each box)'.format(t_i,P))
+    bx.legend(loc='upper left',title='Legend')
+
+    #Loi mathematique
+    print(T_maths)
+    cx = fig.add_subplot(224)
+    cx.bar(x,T_maths, width=1,label='Theoretical values', edgecolor="blue", linewidth=0.7,color='red')
+    cx.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,100), yticks=np.linspace(0, 100, 10))
+    cx.set_ylabel('P(T{}=i)'.format(t_i))
+    cx.set_xlabel('Boxes i=(1-{})'.format(N))
+    cx.set_title('Theoretical T{} values in %'.format(t_i))
+    cx.legend(loc='upper left',title='Legend')
     plt.show()
 
-    #Mathematical P(Ti=k) plot
-    x =  np.arange(N)
-    print(x)
-    ax = fig.add_subplot(122)
-    ax.hist(x,Sum_T, width=1,label='Empirical values', edgecolor="blue", linewidth=0.7,color='red')
-    ax.set(xlim=(0, N), xticks=np.arange(0, N),ylim=(0,3), yticks=np.linspace(0, 3, 5))
-    ax.set_ylabel('Items')
-    ax.set_xlabel('Boxes (1-{})'.format(N))
-    ax.set_title('T histogram for {} packages (Number of packages in each box)'.format(P))
-    ax.legend(loc='upper left',title='Legend')
-    plt.show()
 N = 10 ** 1
 sim = simulate_NFBP(N)
 
@@ -257,10 +279,4 @@ for j in range(sim["i"] + 1):
 
 print()
 stats_NFBP_iter(10**3, 10)
-#stats_NFDBP(10 ** 3, 10)
+stats_NFDBP(10 ** 3, 10,1)
-#
-#pyplot.plot([1, 2, 4, 4, 2, 1], color = 'red', linestyle = 'dashed', linewidth = 2,
-#markerfacecolor = 'blue', markersize = 5)
-#pyplot.ylim(0, 5)
-#pyplot.title('Un exemple')
-#show()