In [1]:
from __future__ import division
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import binom
from pimad.models.toycontinuous import ToyContinuous
from pimad.figures.convergence import *
%matplotlib inline
In [10]:
x = range(101)
z = 1/3
T = 100
y = analytical({"m":1/3,"r":1/3})
plt.plot(x,y,color="red",label="$\hat{z}_1=1/3$",ls = "steps")
ax = plt.gca()
ax.annotate(r'$1-\hat{z}_1$', xy=(0,1-z),xycoords="data", textcoords="offset points",
xytext=(+40,0),
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))
z = 2/3
y = analytical({"m":2/3,"r":2/3})
plt.plot(x,y,color="blue",label="$\hat{z}_2=2/3$",ls = "steps")
ax.annotate(r'$1-\hat{z}_2$', xy=(0,1-z),xycoords="data", textcoords="offset points", xytext=(+40,0),
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))
ax.axis([-5,T,0,1-0.33+0.1])
ax.spines['right'].set_color("none")
ax.spines['top'].set_color("none")
ax.xaxis.set_ticks([1,T])
ax.set_xticklabels(['$1$','$T$'])
ax.yaxis.set_ticks([])
ax.xaxis.set_ticks_position('bottom')
ax.xaxis.set_label_coords(.45, -0.025)
ax.set_xlabel("Group size")
ax.set_ylabel("Density")
plt.legend()
plt.tight_layout()
plt.savefig("sizedistr.eps")
In [ ]:
def sigma(z,T):
s = 0
for n in range(2,T+1):
s += g(n,z+0.001,z,T)/n
return s
T = 100
z = np.arange(0.001,1.001,0.001)
minz = 2.0/z
maxz = [1/sigma(r,T) for r in z]
In [96]:
plt.plot(z,minz, "r",label="$z_{min}$")
plt.plot(z,maxz, "g",label="$z_{max}$")
plt.hlines(T,*plt.xlim())
plt.hlines(2,*plt.xlim())
ax = plt.gca()
ax.semilogy()
plt.xlabel("z")
plt.ylabel("b/c")
plt.xlim((0,1))
plt.ylim((0,1000))
plt.yticks([1,2,10,100,1000],[1,2,10,"T=100",1000])
plt.legend()
Out[96]: