Methodology to distinguish single and double exponential distribution

by Brenlla   Last Updated October 09, 2019 15:19 PM

I have a set of n data points $x = [x_1, x_2,...,x_n]$ that follow an exponential distribution or a double exponential distribution (two different $\lambda$ parameters).

In order to check which distribution works better, I did Maximum Likelihood Estimation (mle) for each of the 2 distribuions. For monoexponential, I followed this method, whereas for the double exponential I used this one.

The problem is I don't know whether x follows a mono or double exponential distribution. Which statistical criteria would be more suited to make a decision?

The following code in Python generates some data x that follows a biexponential distribution with 2:1 relative weights:

import numpy as np
x2 = np.random.exponential(scale=2, size=500)
x5 = np.random.exponential(scale=5, size=1000)
x = np.concatenate([x2, x5])

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