CODEWITHSUNDEEP
pythonstatisticsscipystatsmodels
Simd
Simd

Reputation: 21244

How to get log likelihood for exponential and gamma distributions

I have some data and I can fit a gamma distribution using for example this code taken from Fitting a gamma distribution with (python) Scipy .

import scipy.stats as ss
import scipy as sp

Generate some gamma data:

alpha=5
loc=100.5
beta=22
data=ss.gamma.rvs(alpha,loc=loc,scale=beta,size=10000)    
print(data)
# [ 202.36035683  297.23906376  249.53831795 ...,  271.85204096  180.75026301
#   364.60240242]

Here we fit the data to the gamma distribution:

fit_alpha,fit_loc,fit_beta=ss.gamma.fit(data)
print(fit_alpha,fit_loc,fit_beta)
# (5.0833692504230008, 100.08697963283467, 21.739518937816108)

print(alpha,loc,beta)
# (5, 100.5, 22)

I can also fit an exponential distribution to the same data. I would however like to do a likelihood ratio test. To do this I don't just need to fit the distributions but I also need to return the likelihood. How can you do that in python?

Upvotes: 3

Views: 3141

Answers (1)

Warren Weckesser
Warren Weckesser

Reputation: 114781

You can compute the log-likelihood of data by calling the logpdf method of stats.gamma and then summing the array.

The first bit of code is from your example:

In [63]: import scipy.stats as ss

In [64]: np.random.seed(123)

In [65]: alpha = 5

In [66]: loc = 100.5

In [67]: beta = 22

In [68]: data = ss.gamma.rvs(alpha, loc=loc, scale=beta, size=10000)

In [70]: data
Out[70]: 
array([ 159.73200869,  258.23458137,  178.0504184 , ...,  281.91672824,
        164.77152977,  145.83445141])

In [71]: fit_alpha, fit_loc, fit_beta = ss.gamma.fit(data)

In [72]: fit_alpha, fit_loc, fit_beta
Out[72]: (4.9953385276512883, 101.24295938462399, 21.992307537192605)

Here's how to compute the log-likelihood:

In [73]: loglh = ss.gamma.logpdf(data, fit_alpha, fit_loc, fit_beta).sum()

In [74]: loglh
Out[74]: -52437.410641032831

Upvotes: 6

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