CODEWITHSUNDEEP
pythonnumpyscipystatsmodels
GXR
GXR

Reputation: 95

Anomalies when trying to fit student's t distribution using scipy

I am trying to fit a t distribution to some data that I have. In order to test it out I first tried to generate a sample from a fixed distribution and try to fit on it. Below is the code that I am using.

samp = t.rvs(loc=0, scale=0.6, df=1.3, size=150)

param = t.fit(samp)

x = linspace(-5,5,100)

pdf_fitted = t.pdf(x,loc=param[0],scale=param[1],df=param[2])
pdf = t.pdf(x,loc=0,scale=0.6,df=1.3)

title('Student\'s t Distribution')
plot(x,pdf_fitted,'r-',x,pdf,'b-')
hist(samp, normed=1,alpha=0.3)
show()
print(param)

Now, one would expect that pdf and pdf_fitted be essentially the same. However, that is not the case. When the plots are shown the original and fitted distributions look very different. Moreover, the parameters obtained do not match the ones specified (loc=0, scale=0.6, df=1.3) at all! This confuses me because I am simply adapting the code from http://glowingpython.blogspot.com/2012/07/distribution-fitting-with-scipy.html to work with t distributions. Can someone tell me if there are any nuances with fitting t distributions? Thanks

Upvotes: 2

Views: 3806

Answers (1)

Warren Weckesser
Warren Weckesser

Reputation: 114946

The fit method of scipy.stats.t returns (df, loc, scale), so this line

pdf_fitted = t.pdf(x,loc=param[0],scale=param[1],df=param[2])

should be

pdf_fitted = t.pdf(x, loc=param[1], scale=param[2], df=param[0])

The example that you linked to uses the normal distribution, which doesn't have an additional shape parameter, so in that case, param[0] is the location and param[1] is the scale.

Upvotes: 5

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