Fitting a histogram with python

Question

I have a histogram  H hist my data bins my bin histtype  step  color  r     I can see that the shape is almost gaussian but I would like to fit this histogram with a gaussian function and print the value of the mean and sigma I get  Can you help me

User · Answer

I was a bit puzzled that norm fit apparently only worked with the expanded list of sampled values   I tried giving it two lists of numbers  or lists of tuples  but it only appeared to flatten everything and threat the input as individual samples   Since I already have a histogram based on millions of samples  I didn t want to expand this if I didn t have to  Thankfully  the normal distribution is trivial to calculate  so      histogram is   val count   from math import sqrt  def normfit hist       n s ss   univar hist      mu   s n     var   ss n-mu mu     return  mu  sqrt var    def univar hist       n   0     s   0     ss   0     for v c in hist          n    c         s    c v         ss    c v v     return n  s  ss  I m sure this must be provided by the libraries  but as I couldn t find it anywhere  I m posting this here instead   Feel free to point to the correct way to do it and downvote me  -

User · Answer

Here you have an example working on py2 6 and py3 2   from scipy stats import norm import matplotlib mlab as mlab import matplotlib pyplot as plt    read data from a text file  One number per line arch    test Log 2  ACRatio txt  datos      for item in open arch  r        item   item strip       if item                try              datos append float item           except ValueError              pass    best fit of data  mu  sigma    norm fit datos     the histogram of the data n  bins  patches   plt hist datos  60  normed 1  facecolor  green   alpha 0 75     add a  best fit  line y   mlab normpdf  bins  mu  sigma  l   plt plot bins  y   r--   linewidth 2    plot plt xlabel  Smarts   plt ylabel  Probability   plt title r   mathrm Histogram  of  IQ     mu   3f    sigma   3f     mu  sigma   plt grid True   plt show

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Starting Python 3 8  the standard library provides the NormalDist object as part of the statistics module   The NormalDist object can be built from a set of data with the NormalDist from samples method and provides access to its mean  NormalDist mean  and standard deviation  NormalDist stdev    from statistics import NormalDist    data    0 7237248252340628  0 6402731706462489  -1 0616113628912391  -1 7796451823371144  -0 1475852030122049  0 5617952240065559  -0 6371760932160501  -0 7257277223562687  1 699633029946764  0 2155375969350495  -0 33371076371293323  0 1905125348631894  -0 8175477853425216  -1 7549449090704003  -0 512427115804309  0 9720486316086447  0 6248742504909869  0 7450655841312533  -0 1451632129830228  -1 0252663611514108  norm   NormalDist from samples data    NormalDist mu -0 12836704320073597  sigma 0 9240861018557649  norm mean   -0 12836704320073597 norm stdev   0 9240861018557649

User · Answer

Here is an example that uses scipy optimize to fit a non-linear functions like a Gaussian  even when the data is in a histogram that isn t well ranged  so that a simple mean estimate would fail   An offset constant also would cause simple normal statistics to fail   just remove p 3  and c 3  for plain gaussian data    from pylab import   from numpy import loadtxt from scipy optimize import leastsq  fitfunc    lambda p  x  p 0  exp -0 5   x-p 1   p 2    2  p 3  errfunc    lambda p  x  y   y - fitfunc p  x    filename    gaussdata csv  data       loadtxt filename skiprows 1 delimiter      xdata      data   0  ydata      data   1   init     1 0  0 5  0 5  0 5   out     leastsq  errfunc  init  args  xdata  ydata   c   out 0   print  A exp -0 5  x-mu  sigma  2    k   print  Parent Coefficients   print  1 000  0 200  0 300  0 625  print  Fit Coefficients   print c 0  c 1  abs c 2   c 3   plot xdata  fitfunc c  xdata   plot xdata  ydata   title r  A     3f    mu     3f    sigma     3f  k     3f      c 0  c 1  abs c 2   c 3      show     Output   A exp -0 5  x-mu  sigma  2    k  Parent Coefficients  1 000  0 200  0 300  0 625 Fit Coefficients  0 961231625289 0 197254597618 0 293989275502 0 65370344131

User · Answer

Here is another solution using only matplotlib pyplot and numpy packages  It works only for Gaussian fitting  It is based on maximum likelihood estimation and have already been mentioned in this topic  Here is the corresponding code      Python version   2 7 9 from   future   import division import numpy as np from matplotlib import pyplot as plt    For the explanation  I simulate the data   N 1000 data   np random randn N    But in reality  you would read data from file  for example with    data   np loadtxt  data txt      Empirical average and variance are computed avg   np mean data  var   np var data    From that  we know the shape of the fitted Gaussian  pdf x   np linspace np min data  np max data  100  pdf y   1 0 np sqrt 2 np pi var  np exp -0 5  pdf x-avg   2 var     Then we plot   plt figure   plt hist data 30 normed True  plt plot pdf x pdf y  k--   plt legend   Fit   Data    best   plt show     and here is the output

[python] Fitting a histogram with python

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