Python - Matplotlib: normalize axis when plotting a Probability Density Function

Question

I'm using Python and some of its extensions to get and plot the Probability Density Function. While I manage to plot it, in its form, at least, I don't manage to succeed on scalating the axis.

import decimal
import numpy as np
import scipy.stats as stats
import pylab as pl
import matplotlib.pyplot as plt
from decimal import *
from scipy.stats import norm

lines=[]

fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = norm.stats(moments='mvsk')

#Here I delete some lines aimed to fill the list with values

Long = len(lines)
Maxim = max(lines) #MaxValue
Minim = min(lines) #MinValue
av = np.mean(lines) #Average
StDev = np.std(lines) #Standard Dev.

x = np.linspace(Minim, Maxim, Long)
ax.plot(x, norm.pdf(x, av, StDev),'r-', lw=3, alpha=0.9, label='norm pdf')

weights = np.ones_like(lines)/len(lines)

ax.hist(lines, weights = weights, normed=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()

The result is

While I would like to have it expressed - In the x-axis centered in 0 and related to the standard deviation - In the y-axis, related to the histogram and the %s (normalized to 1)
For the x-axis as the image below

And like this last image for the y-axis

I've managed to escalate the y-axis in a histogram by plotting it individually with the instruction weights = weights and setting it into the plot, but I can't do it here. I include it in the code but actually it does nothing in this case.

Any help would be appreciated

Answer 1

the y-axis is normed in a way, that the area under the curve is one. And adding equal weights for every data point makes no sense if you normalize anyway with normed=True.

first you need to shift your data to 0:

 lines -= mean(lines)

then plot it.

ythis should be a working minimal example:

import numpy as np                                                               
from numpy.random import normal                                                  
import matplotlib.pyplot as plt
from scipy.stats import norm                                                  

# gaussian distributed random numbers with mu =4 and sigma=2                     
x = normal(4, 2, 10000)                                                            

mean = np.mean(x)
sigma = np.std(x)

x -= mean 

x_plot = np.linspace(min(x), max(x), 1000)                                                               

fig = plt.figure()                                                               
ax = fig.add_subplot(1,1,1)                                                      

ax.hist(x, bins=50, normed=True, label="data")
ax.plot(x_plot, norm.pdf(x_plot, mean, sigma), 'r-', label="pdf")                                                          

ax.legend(loc='best')

x_ticks = np.arange(-4*sigma, 4.1*sigma, sigma)                                  
x_labels = [r"${} \sigma$".format(i) for i in range(-4,5)]                       

ax.set_xticks(x_ticks)                                                           
ax.set_xticklabels(x_labels)                                                     

plt.show() 

output image is this:

and you have too much imports. you import decimals twice, one time even with * and then numpy, pyplot and scipy are included in pylab. Also why import the whole scipy.stats and then again import just norm from it?