In [1]:
'''
author: Alvason Zhenhua Li
date: 03/19/2015
'''
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import os
dir_path = '/Users/al/Desktop/GitHub/probability-insighter/figure'
file_name = 'logistic-distribution'
import alva_machinery_probability as alva
AlvaFontSize = 23
AlvaFigSize = (16, 7)
numberingFig = 0
# plotting
figure_name = '-equation'
file_suffix = '.png'
save_figure = os.path.join(dir_path, file_name + figure_name + file_suffix)
numberingFig = numberingFig + 1
plt.figure(numberingFig, figsize=(9, 6))
plt.axis('off')
plt.title(r'$ Logistic-distribution---probability-density-function $',fontsize = AlvaFontSize)
plt.text(0, 5.0/6, r'$ P(d, m|x) = \frac{exp[-\frac{(x - m)}{d}]}{d(1 - exp[-\frac{(x - m)}{d}])^2} $',
fontsize = 1.2*AlvaFontSize)
plt.text(0, 3.0/6, r'$ 1-- \ m \ is \ the \ mean \ number \ of \ events \ per \ interval \ (time \ or \ space) $',
fontsize = AlvaFontSize)
plt.text(0, 2.0/6, r'$ 2-- \ d \ is \ the \ deviation \ with \ n-events \ per \ interval $', fontsize = AlvaFontSize)
plt.text(0, 1.0/6, r'$ 3-- \ P(d, m|x) \ is \ the \ probability \ with \ n-events \ per \ interval $',
fontsize = AlvaFontSize)
plt.savefig(save_figure, dpi = 300)
plt.show()
In [2]:
'''Logistic randomness --- Logistic distribution'''
totalPoint_Input = int(100 + 1)
gInput = np.arange(totalPoint_Input)
meanL = totalPoint_Input/2
randomSeed_normal = np.random.standard_normal(totalPoint_Input)
randomSeed = np.random.logistic(0, 3, totalPoint_Input)
totalLevel = int(totalPoint_Input/1)
category = alva.AlvaLevel(randomSeed, totalLevel, False)
gLevel = category[0]
numberLevel = category[1]
print category[2].shape
# calculating the mean
sumL = 0
for i in range(totalPoint_Input):
sumL = sumL + randomSeed[i]
current_mean = sumL/(totalPoint_Input)
print ('current mean', current_mean)
totalLevel = int(totalPoint_Input/1)
category_normal = alva.AlvaLevel(randomSeed_normal, totalLevel, False)
gLevel_normal = category_normal[0]
numberLevel_normal = category_normal[1]
category = alva.AlvaLevel(randomSeed, totalLevel, False)
gLevel = category[0]
numberLevel = category[1]
print category[2].shape
# plotting
figure_name = ''
file_suffix = '.png'
save_figure = os.path.join(dir_path, file_name + figure_name + file_suffix)
numberingFig = numberingFig + 1
figure = plt.figure(numberingFig, figsize = AlvaFigSize)
plot1 = figure.add_subplot(1, 2, 1)
plot1.plot(gInput, randomSeed, color = 'gray', marker = 'o', label = 'data')
plot1.plot(gInput, alva.AlvaMinMax(randomSeed), color = 'red', marker = 'o', label = 'minMaxListing')
plot1.plot(gInput, alva.AlvaMinMax(randomSeed_normal), label = 'minMax_normal')
if totalPoint_Input < 100:
plot1.set_xticks(gInput, minor = True)
plot1.set_yticks(randomSeed, minor = True)
plot1.grid(True, which = 'minor')
else:
plot1.grid(True, which = 'major')
plt.title(r'$ Logistic (total-input = %i,\ mean = %f) $'%(totalPoint_Input, meanL)
, fontsize = AlvaFontSize)
plt.xlabel(r'$ input-time $', fontsize = AlvaFontSize)
plt.ylabel(r'$ output $', fontsize = AlvaFontSize)
plt.legend(loc = (0, -0.2))
plot2 = figure.add_subplot(1, 2, 2)
plot2.plot(numberLevel_normal, gLevel_normal, label = 'category_normal')
plot2.plot(numberLevel, gLevel, color = 'red', marker = 'o', label = 'category')
if totalPoint_Input < 100:
plot2.set_xticks(numberLevel, minor = True)
plot2.set_yticks(gLevel, minor = True)
plot2.grid(True, which = 'minor')
else:
plot2.grid(True, which = 'major')
plt.title(r'$ Logistic \ distribution\ (data = %i,\ level = %i) $'%(totalPoint_Input, totalLevel)
, fontsize = AlvaFontSize)
plt.xlabel(r'$ Number/level $', fontsize = AlvaFontSize)
plt.ylabel(r'$ Output-level $', fontsize = AlvaFontSize)
plt.legend(loc = (0, -0.2))
figure.tight_layout()
plt.savefig(save_figure, dpi = 300)
plt.show()
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