# Fit a distribution by maximum likelihood¶

In this example we are going to estimate the parameters of a parametric by generic numerical optimization of the likelihood.

The likelihood of a sample according to a parametric density function is: from __future__ import print_function
import openturns as ot
import math as m
ot.Log.Show(ot.Log.NONE)


Create data from a gaussian pdf with mu=4, sigma=1.5

sample = ot.Normal(4.0, 1.5).getSample(200)


Create the search interval of (mu, sigma): the constraint is sigma>0

lowerBound = [-1.0, 1.0e-4]
upperBound = [-1.0, -1.0]
finiteLowerBound = [False, True]
finiteUpperBound = [False, False]
bounds = ot.Interval(lowerBound, upperBound, finiteLowerBound, finiteUpperBound)


Create the starting point of the research For mu : the first point For sigma : a value evaluated from the two first points

mu0 = sample
sigma0 = m.sqrt((sample - sample) * (sample - sample))
startingPoint = [mu0, sigma0]
ot.Point(startingPoint)


[2.39784,4.01969]

Create the estimator from a parametric pdf

pdf = ot.Normal()
factory = ot.MaximumLikelihoodFactory(pdf)
factory.setOptimizationBounds(bounds)


Set the starting point via the solver

solver = factory.getOptimizationAlgorithm()
solver.setStartingPoint(startingPoint)
factory.setOptimizationAlgorithm(solver)


Estimate the parametric model

distribution = factory.build(sample)
str(distribution)


Out:

'Normal(mu = 3.94775, sigma = 1.49821)'


Retrieve the estimated parameters

distribution.getParameter()


[3.94775,1.49821]

Total running time of the script: ( 0 minutes 0.004 seconds)

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