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])