Plot a density function above a histogram - python

In Python, I have estimated the parameters for the density of a model of my distribution and I would like to plot the density function above the histogram of the distribution. In R it is similar to using the option prop=TRUE.
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
# initialization of the list "data"
# estimation of the parameter, in my case, mean and variance of a normal distribution
plt.hist(data, bins="auto") # data is the list of data
# here I would like to draw the density above the histogram
plt.show()
I guess the trickiest part is to make it fit.
Edit: I have tried this according to the first answer:
mean = np.mean(logdata)
var = np.var(logdata)
std = np.sqrt(var) # standard deviation, used by numpy as a replacement of the variance
plt.hist(logdata, bins="auto", alpha=0.5, label="données empiriques")
x = np.linspace(min(logdata), max(logdata), 100)
plt.plot(x, mlab.normpdf(x, mean, std))
plt.xlabel("log(taille des fichiers)")
plt.ylabel("nombre de fichiers")
plt.legend(loc='upper right')
plt.grid(True)
plt.show()
But it doesn't fit the graph, here is how it looks:
** Edit 2 ** Works with the option normed=True in the histogram function.


If I understand you correctly you have the mean and standard deviation of some data. You have plotted a histogram of this and would like to plot the normal distribution line over the histogram. This line can be generated using matplotlib.mlab.normpdf(), the documentation can be found here.
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
mean = 100
sigma = 5
data = np.random.normal(mean,sigma,1000) # generate fake data
x = np.linspace(min(data), max(data), 100)
plt.hist(data, bins="auto",normed=True)
plt.plot(x, mlab.normpdf(x, mean, sigma))
plt.show()
Which gives the following figure:
Edit: The above only works with normed = True. If this is not an option, we can define our own function:
def gauss_function(x, a, x0, sigma):
return a * np.exp(-(x - x0) ** 2 / (2 * sigma ** 2))
mean = 100
sigma = 5
data = np.random.normal(mean,sigma,1000) # generate fake data
x = np.linspace(min(data), max(data), 1000)
test = gauss_function(x, max(data), mean, sigma)
plt.hist(data, bins="auto")
plt.plot(x, test)
plt.show()


All what you are looking for, already are in seaborn.
You just have to use distplot
import seaborn as sns
import numpy as np
data = np.random.normal(5, 2, size=1000)
sns.distplot(data)

Related

Problem to fit a poisson histogram in python

I'm trying to fit some data with a poisson distribution, but it doesn't work.
x = [46,71,106,126,40,27,19,103,46,89,31,70,35,43,82,128,185,47,18,36,96,30,135,36,40,72,32,86,76,116,51,23,40,121,22,107,65,93,25,74,73,73,111,56,34,28,87,14,70,54,63,50,89,62,35,59,71,39,23,46,32,56,15,68,30,69,37,41,43,106,20,35,63,44,40,32,102,28,54,32,42,19,69,31,36,86,41,57,39,53,48,121,35,51,10,68,14,140,57,50,178,37,121,35,206,26,54,5,53,17,139,49,122,110,62,81,43,83,47,62,2,50,36,190,32,124,89,60,39,156,89,26,57,34,58,29,22,96,132,59,34,43,50,58,48,56,43,54,22,26,60,43,69,58,100,122,48,55,29,55,57,36,42,51,24,81,66,73,112,34,54,45,29,53,43,60,72,13,72,85,49,80,47,40,28,43,37,48,31,60,33,75,53,71,49,142,47,28,51,80,50,33,67,28,101,80,60,80,98,39,69,27,32,11,32,62,32,77,110,45,61,22,23,73,25,27,41,42,65,23,127,128,42,44,10,50,56,73,42,63,70,148,18,109,111,54,34,18,32,50,100,41,39,58,93,42,86,70,41,27,24,57,77,81,101,48,52,146,59,87,86,120,28,23,76,52,59,31,60,32,65,49,27,106,136,23,15,77,44,96,62,66,26,41,70,13,64,124,49,44,55,68,54,58,72,41,21,80,3,49,54,35,48,38,83,59,36,80,47,32,38,16,43,196,19,80,28,56,23,81,103,45,25,42,44,34,106,23,47,53,119,56,54,108,35,20,34,39,70,61,40,35,51,104,63,55,93,22,32,48,20,121,55,76,36,32,121,58,42,101,32,49,77,23,95,32,75,53,106,194,54,31,104,69,58,66,29,66,37,28,59,60,70,95,63,103,173,47,59,27] #geiger count
bins = np.histogram_bin_edges(x)
n, bins_edges, patches = plt.hist(x,bins, density=1, facecolor='darkblue',ec='white', log=0)
print(n)
bin_middles = 0.5*(bins_edges[1:] + bins_edges[:-1])
def fit_function(k, lamb):
return poisson.pmf(k, lamb)
parameters, cov_matrix = curve_fit(fit_function, bin_middles,n)
x_plot = np.arange(0,max(x))
plt.plot(x_plot,fit_function(x_plot, *parameters),label='Poisson')
plt.show()
I'm getting this as result but as we can see it's not right

You are using functions such as np.histogram_bin_edges meant for continuous distributions, while the Poisson distribution is discrete.
According to wikipedia, lambda can be estimated by just taking the mean of the samples:
from scipy.stats import poisson
import numpy as np
from matplotlib import pyplot as plt
x = [46,71,106,126,40,27,19,103,46,89,31,70,35,43,82,128,185,47,18,36,96,30,135,36,40,72,32,86,76,116,51,23,40,121,22,107,65,93,25,74,73,73,111,56,34,28,87,14,70,54,63,50,89,62,35,59,71,39,23,46,32,56,15,68,30,69,37,41,43,106,20,35,63,44,40,32,102,28,54,32,42,19,69,31,36,86,41,57,39,53,48,121,35,51,10,68,14,140,57,50,178,37,121,35,206,26,54,5,53,17,139,49,122,110,62,81,43,83,47,62,2,50,36,190,32,124,89,60,39,156,89,26,57,34,58,29,22,96,132,59,34,43,50,58,48,56,43,54,22,26,60,43,69,58,100,122,48,55,29,55,57,36,42,51,24,81,66,73,112,34,54,45,29,53,43,60,72,13,72,85,49,80,47,40,28,43,37,48,31,60,33,75,53,71,49,142,47,28,51,80,50,33,67,28,101,80,60,80,98,39,69,27,32,11,32,62,32,77,110,45,61,22,23,73,25,27,41,42,65,23,127,128,42,44,10,50,56,73,42,63,70,148,18,109,111,54,34,18,32,50,100,41,39,58,93,42,86,70,41,27,24,57,77,81,101,48,52,146,59,87,86,120,28,23,76,52,59,31,60,32,65,49,27,106,136,23,15,77,44,96,62,66,26,41,70,13,64,124,49,44,55,68,54,58,72,41,21,80,3,49,54,35,48,38,83,59,36,80,47,32,38,16,43,196,19,80,28,56,23,81,103,45,25,42,44,34,106,23,47,53,119,56,54,108,35,20,34,39,70,61,40,35,51,104,63,55,93,22,32,48,20,121,55,76,36,32,121,58,42,101,32,49,77,23,95,32,75,53,106,194,54,31,104,69,58,66,29,66,37,28,59,60,70,95,63,103,173,47,59,27] bins = np.histogram_bin_edges(x)
n, bins_edges, patches = plt.hist(x, bins, density=1, facecolor='darkblue', ec='white', log=0)
lamd = np.mean(x)
x_plot = np.arange(0, max(x) + 1)
plt.plot(x_plot, poisson.pmf(x_plot, lamd), label='Poisson')
plt.show()
The calculated lambda is about 60. The plot seems to indicate that the Poisson distribution isn't a very close fit for the given samples.

Draw the density curve exactly on the Histogram without normalizing

I need to draw the density curve on the Histogram with the actual height of the bars (actual frequency) as the y-axis.
Try1:
I found a related answer here but, it has normalized the Histogram to the range of the curve.
Below is my code and the output.
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
from scipy.stats import norm
data = [125.36, 126.66, 130.28, 133.74, 126.92, 120.85, 119.42, 128.61, 123.53, 130.15, 126.02, 116.65, 125.24, 126.84,
125.95, 114.41, 138.62, 127.4, 127.59, 123.57, 133.76, 124.6, 113.48, 128.6, 121.04, 119.42, 120.83, 136.53, 120.4,
136.58, 121.73, 132.72, 109.25, 125.42, 117.67, 124.01, 118.74, 128.99, 131.11, 112.27, 118.76, 119.15, 122.42,
122.22, 134.71, 126.22, 130.33, 120.52, 126.88, 117.4]
(mu, sigma) = norm.fit(data)
x = np.linspace(min(data), max(data), 100)
plt.hist(data, bins=12, normed=True)
plt.plot(x, mlab.normpdf(x, mu, sigma))
plt.show()
Try2:
There #DavidG has given an option, a user defined function even it doesn't cover the density of the Histogram accurately.
def gauss_function(x, a, x0, sigma):
return a * np.exp(-(x - x0) ** 2 / (2 * sigma ** 2))
test = gauss_function(x, max(data), mu, sigma)
plt.hist(data, bins=12)
plt.plot(x, test)
plt.show()
The result for this was,
But the actual Histogram is below, where Y-axis ranges from 0 to 8,
And I want to draw the density curve exactly on that. Any help this regards will be really appreciated.

Is this what you're looking for? I'm multiplying the pdf by the area of the histogram.
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
data = [125.36, 126.66, 130.28, 133.74, 126.92, 120.85, 119.42, 128.61, 123.53, 130.15, 126.02, 116.65, 125.24, 126.84,
125.95, 114.41, 138.62, 127.4, 127.59, 123.57, 133.76, 124.6, 113.48, 128.6, 121.04, 119.42, 120.83, 136.53, 120.4,
136.58, 121.73, 132.72, 109.25, 125.42, 117.67, 124.01, 118.74, 128.99, 131.11, 112.27, 118.76, 119.15, 122.42,
122.22, 134.71, 126.22, 130.33, 120.52, 126.88, 117.4]
(mu, sigma) = norm.fit(data)
x = np.linspace(min(data), max(data), 100)
values, bins, _ = plt.hist(data, bins=12)
area = sum(np.diff(bins) * values)
plt.plot(x, norm.pdf(x, mu, sigma) * area, 'r')
plt.show()
Result:

Fit histogram log scale python

I need to fit a curve with my histogram in python. I did this before with normal histograms, this time I am trying to do the same with a logarithmic plot in x.
This is my code:
import numpy as np
import matplotlib.pyplot as plt
//radius is my np.array
Rmin = min(radius)
Rmax = max(radius)
logmin = np.log(Rmin)
logmax = np.log(Rmax)
bins = 10**(np.arange(logmin,logmax,0.1))
plt.figure()
plt.xscale("log")
plt.hist(radius, bins, color = 'red')
plt.show()
This is showing a gaussian distribution. I am trying to fit a curve with it and what I did is computing the following before the show() command.
(mu, sigma) = np.log(norm.fit((radius)))
y = (mlab.normpdf(np.log(bins), mu, sigma))
plt.plot(bins, y, 'b--', linewidth=2)
My result is a very flattened curve with respect to my distribution.
Can someone help me?
I can not add the whole array r(50000 points), therefore I have added a picture showing my result. See image

Fitting Maxwell-Boltzman distribution in Python

Is it possible to make a fit to Maxwell-Boltzmann like data in matplotlib or similar module in python?

scipy.stats has support for the maxwell distribution.
import scipy.stats as stats
import matplotlib.pyplot as plt
import numpy as np
maxwell = stats.maxwell
data = maxwell.rvs(loc=0, scale=5, size=10000)
params = maxwell.fit(data, floc=0)
print(params)
# (0, 4.9808603062591041)
plt.hist(data, bins=20, normed=True)
x = np.linspace(0, 25, 100)
plt.plot(x, maxwell.pdf(x, *params), lw=3)
plt.show()
The first parameter is the location or shift away from zero.
The second parameter is the scaling parameter, denoted by a on the wikipedia page.
To generate random variates (random data) with this distribution, use its rvs method:
newdata = maxwell.rvs(*params, size=100)

python: plotting a histogram with a function line on top

I'm trying to do a little bit of distribution plotting and fitting in Python using SciPy for stats and matplotlib for the plotting. I'm having good luck with some things like creating a histogram:
seed(2)
alpha=5
loc=100
beta=22
data=ss.gamma.rvs(alpha,loc=loc,scale=beta,size=5000)
myHist = hist(data, 100, normed=True)
Brilliant!
I can even take the same gamma parameters and plot the line function of the probability distribution function (after some googling):
rv = ss.gamma(5,100,22)
x = np.linspace(0,600)
h = plt.plot(x, rv.pdf(x))
How would I go about plotting the histogram myHist with the PDF line h superimposed on top of the histogram? I'm hoping this is trivial, but I have been unable to figure it out.

just put both pieces together.
import scipy.stats as ss
import numpy as np
import matplotlib.pyplot as plt
alpha, loc, beta=5, 100, 22
data=ss.gamma.rvs(alpha,loc=loc,scale=beta,size=5000)
myHist = plt.hist(data, 100, normed=True)
rv = ss.gamma(alpha,loc,beta)
x = np.linspace(0,600)
h = plt.plot(x, rv.pdf(x), lw=2)
plt.show()
to make sure you get what you want in any specific plot instance, try to create a figure object first
import scipy.stats as ss
import numpy as np
import matplotlib.pyplot as plt
# setting up the axes
fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111)
# now plot
alpha, loc, beta=5, 100, 22
data=ss.gamma.rvs(alpha,loc=loc,scale=beta,size=5000)
myHist = ax.hist(data, 100, normed=True)
rv = ss.gamma(alpha,loc,beta)
x = np.linspace(0,600)
h = ax.plot(x, rv.pdf(x), lw=2)
# show
plt.show()

One could be interested in plotting the distibution function of any histogram.
This can be done using seaborn kde function
import numpy as np # for random data
import pandas as pd # for convinience
import matplotlib.pyplot as plt # for graphics
import seaborn as sns # for nicer graphics
v1 = pd.Series(np.random.normal(0,10,1000), name='v1')
v2 = pd.Series(2*v1 + np.random.normal(60,15,1000), name='v2')
# plot a kernel density estimation over a stacked barchart
plt.figure()
plt.hist([v1, v2], histtype='barstacked', normed=True);
v3 = np.concatenate((v1,v2))
sns.kdeplot(v3);
plt.show()
from a coursera course on data visualization with python

Expanding on Malik's answer, and trying to stick with vanilla NumPy, SciPy and Matplotlib. I've pulled in Seaborn, but it's only used to provide nicer defaults and small visual tweaks:
import numpy as np
import scipy.stats as sps
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(style='ticks')
# parameterise our distributions
d1 = sps.norm(0, 10)
d2 = sps.norm(60, 15)
# sample values from above distributions
y1 = d1.rvs(300)
y2 = d2.rvs(200)
# combine mixture
ys = np.concatenate([y1, y2])
# create new figure with size given explicitly
plt.figure(figsize=(10, 6))
# add histogram showing individual components
plt.hist([y1, y2], 31, histtype='barstacked', density=True, alpha=0.4, edgecolor='none')
# get X limits and fix them
mn, mx = plt.xlim()
plt.xlim(mn, mx)
# add our distributions to figure
x = np.linspace(mn, mx, 301)
plt.plot(x, d1.pdf(x) * (len(y1) / len(ys)), color='C0', ls='--', label='d1')
plt.plot(x, d2.pdf(x) * (len(y2) / len(ys)), color='C1', ls='--', label='d2')
# estimate Kernel Density and plot
kde = sps.gaussian_kde(ys)
plt.plot(x, kde.pdf(x), label='KDE')
# finish up
plt.legend()
plt.ylabel('Probability density')
sns.despine()
gives us the following plot:
I've tried to stick with a minimal feature set while producing relatively nice output, notably using SciPy to estimate the KDE is very easy.

Categories

Resources