In [2]:

    

#this cell was taken and adjusted from http://nbviewer.ipython.org/github/cs109/content/blob/master/HW3_solutions.ipynb
%matplotlib inline 

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import random

from scipy.stats import pearsonr


# set some nicer defaults for matplotlib
from matplotlib import rcParams

#colorbrewer2 Dark2 qualitative color table
dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),
                (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),
                (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),
                (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),
                (0.4, 0.6509803921568628, 0.11764705882352941),
                (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),
                (0.6509803921568628, 0.4627450980392157, 0.11372549019607843)]

rcParams['figure.figsize'] = (12, 6.5)
rcParams['figure.dpi'] = 150
rcParams['axes.color_cycle'] = dark2_colors
rcParams['lines.linewidth'] = 2
rcParams['axes.facecolor'] = 'white'
rcParams['font.size'] = 18
rcParams['patch.edgecolor'] = 'white'
rcParams['patch.facecolor'] = dark2_colors[0]
rcParams['font.family'] = 'StixGeneral'

def remove_border(axes=None, top=False, right=False, left=True, bottom=True):
    """
    Minimize chartjunk by stripping out unnecesary plot borders and axis ticks
    
    The top/right/left/bottom keywords toggle whether the corresponding plot border is drawn
    """
    ax = axes or plt.gca()
    ax.spines['top'].set_visible(top)
    ax.spines['right'].set_visible(right)
    ax.spines['left'].set_visible(left)
    ax.spines['bottom'].set_visible(bottom)
    
    #turn off all ticks
    ax.yaxis.set_ticks_position('none')
    ax.xaxis.set_ticks_position('none')
    
    #now re-enable visibles
    if top:
        ax.xaxis.tick_top()
    if bottom:
        ax.xaxis.tick_bottom()
    if left:
        ax.yaxis.tick_left()
    if right:
        ax.yaxis.tick_right()


    

In [3]:

    

#Produktdaten über Zeit 
menge_vk = [round(random.normalvariate(1000, 40)) for _ in xrange(48*30)]
preis_prod = [random.normalvariate(100, 5) for _ in xrange(48*30)]
umsatz = [a*b for a,b in zip(menge_vk,preis_prod)]

sales_df = pd.DataFrame({"Menge": menge_vk, "Preis": preis_prod, "Umsatz": umsatz})


    

In [4]:

    

#plot sold quantities
sales_df['Menge'].hist(bins=20)
remove_border()
plt.grid(False)
plt.grid(axis = 'y', color ='white', linestyle='-')
plt.title('Verteilung der verkauften Mengen')
plt.ylabel('Anzahl')
plt.xlabel('Menge')

plt.show()


    

In [14]:

    

#plot prices
sales_df['Preis'].hist(bins=20, color=dark2_colors[1])
remove_border()
plt.grid(False)
plt.grid(axis = 'y', color ='white', linestyle='-')
plt.title('Verteilung der Preise')
plt.ylabel('Anzahl')
plt.xlabel('Preis')

plt.show()


    

In [15]:

    

#plot revenue
sales_df['Umsatz'].hist(bins=50, color=dark2_colors[2])
remove_border()
plt.grid(False)
plt.grid(axis = 'y', color ='white', linestyle='-')
plt.title('Verteilung des Umsatzes')
plt.ylabel('Anzahl')
plt.xlabel('Umsatz')

plt.show()


    

In [16]:

    

#aggregate monthly revenue
monthly_sales = []
count = 0
zwischensumme = 0
for k, v in sales_df['Umsatz'].iterkv():
    count +=1
    zwischensumme += v
    if count == 30:
        count = 0
        monthly_sales.append(zwischensumme)
        zwischensumme = 0


    

In [17]:

    

#plot development of monthly revenue 
plt.plot(monthly_sales, color=dark2_colors[2])
remove_border()
plt.title('Entwicklung des monatlichen Umsatzes')
plt.ylabel('Umsatz')
plt.xlabel('Monat nr.')

plt.show()


    

In [9]:

    

#Analysis Part 1
#Es wird eine gleichverteilung angenommen
print "Durchschnittswerte"
print sales_df.mean()
print "-------------"
print 
print "Standardabweichungen"
print sales_df.std()


    

    




Durchschnittswerte
Menge        998.038194
Preis        100.342317
Umsatz    100145.983396
dtype: float64
-------------

Standardabweichungen
Menge       39.884971
Preis        4.920678
Umsatz    6347.807416
dtype: float64

In [10]:

    

#error graphs
mengenfehler = sales_df['Menge'].apply(lambda x: x-sales_df['Menge'].mean())
preisfehler = sales_df['Preis'].apply(lambda x: x-sales_df['Preis'].mean())
umsatzfehler = sales_df['Umsatz'].apply(lambda x: x-sales_df['Umsatz'].mean())



f, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True)

ax1.hist(mengenfehler)
ax1.grid(False)
ax1.grid(axis = 'y', color ='white', linestyle='-')
ax1.spines['top'].set_visible(False)
ax1.spines['right'].set_visible(False)

ax2.hist(preisfehler)
ax2.grid(False)
ax2.grid(axis = 'y', color ='white', linestyle='-')
ax2.spines['top'].set_visible(False)
ax2.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)

ax3.hist(umsatzfehler)
ax3.grid(False)
ax3.grid(axis = 'y', color ='white', linestyle='-')
ax3.spines['top'].set_visible(False)
ax3.spines['right'].set_visible(False)
ax3.spines['left'].set_visible(False)


plt.show()


    

In [18]:

    

#bootstrapping zum finden der Sicherheit bei 1100 Lagereinheiten

def bootstrap_mengensicherheit(nsample=1000, show_1100=True):
    schaetzung = sales_df['Menge'].mean()
    
    error_samples = [random.choice(mengenfehler) for _ in xrange(nsample)]
    
    predictions = schaetzung+error_samples
    
    if show_1100:
        count_below = 0
        for i in predictions:
            if i<1100:
                count_below+=1
        print "Wahrscheinlichkeit, dass weniger als 1.100 Einheiten verkauft wird:", count_below/float(nsample)*100, "%"
    else:
        return predictions
    
    
    
bootstrap_mengensicherheit()


    

    




Wahrscheinlichkeit, dass weniger als 1.100 Einheiten verkauft wird: 99.7 %

In [12]:

    

#finde 95% confidence nummer

def bootstrap_get_confidence(chance=95):
    pred = bootstrap_mengensicherheit(show_1100=False)
    
    return np.percentile(np.array(pred), chance)


    

In [13]:

    

bootstrap_get_confidence(chance=95)


    

    
Out[13]:





1067.05