F-test for the difference in means between two samples from exponential distributions

f_test_expon_means.py

#This two-sided test compares the means of two samples coming from exponential distributions, and returns a p-value.
#It is generally more powerful than the Welch's t-test or the regular t-test, when sample sizes are equal.
#Avoid using it if sample sizes are unequal.

from scipy import stats
import numpy as np
import warnings

#Function to conduct the test
def f_test_expon_means(x, y):
    #x is the first sample, y the second sample
    ratio = np.mean(x) / np.mean(y)
    n_x = len(x)
    n_y = len(y)
    if n_x != n_y:
        warnings.warn("The sample sizes are unequal. Consider using the Welch's t-test instead: `stats.ttest_ind(x, y, equal_var=False)`")
    pval = 1 - stats.f.sf(ratio, n_x*2, n_y*2)
    pval = 2 * min([pval, 1-pval])
    
    return pval

#Example:
#we generate two random sample with an exponential distribution, x and y:
x = stats.expon(scale=2).rvs(size=200, random_state=0)
y = stats.expon(scale=1.5).rvs(size=200, random_state=0)
#then we use the function on these two samples:
f_test_expon_means(x,y)
#0.0041035208895015
#And that's it!

#Simulation to compare power of Welch's t-test to the power of the F-test for means, with an alpha level of 0.05      
#The sample sizes here are equal (150), so the F-test is a bit more powerful here
results_f = []
results_t = []
a = stats.expon(scale=1.5)
b = stats.expon(scale=1)

for i in range(10000):
    x = a.rvs(150)
    y = b.rvs(150)
    p_f = f_test_expon_means(x,y)
    results_f.append(p_f)
    p_t = stats.ttest_ind(x, y, equal_var=False).pvalue
    results_t.append(p_t)
    
results_f = np.array(results_f)
print("power of the F-test:", np.mean(results_f<0.05))
results_t = np.array(results_t)
print("power of the Welch's t-test:", np.mean(results_t<0.05))