python - Plotting a skewed distribution from mean, starting, and end value

Question

I have a the following data:

starting_point = 0.00000016
mean = 0.000351
end_point = 0.75

Is it correct to use this to determine the skew?

from scipy.stats import skew
skew([0.00000016, 0.000351, 0.75])

>> 0.7071062587209218

How can I plot a distribution to show the skewed distribution in python 3?

Answer 1

You have calculated the skewness of the three datapoints. As two are rather small compared to the third the skewness is positive. Its trickier to fit a distribution through data (especially just three points). You can refer to fitting empirical distributions for an exhaustive description.

Just as an example of how a distribution might look like which is skewed (as your data suggests; I have chosen a gamma-distribution - careful: the actual fitting is much more complicated, refer to the answer above; this is just to show the difference):

from scipy import stats
import numpy as np
import matplotlib.pyplot as plt

starting_point = 0.00000016
mean = 0.000351
end_point = 0.75

data = [starting_point, mean, end_point]
print('skewness of data:', skew(data))

a, loc, scl = stats.gamma.fit(data)

x = np.arange(starting_point, end_point, 0.0002635)
plt.plot(x, stats.gamma.pdf(x, a, loc, scl))

plt.show()

dvals = [val for val in stats.gamma.pdf(x, a, loc, scl)]

print('skewness of distribution:', skew(dvals))

will result in a different skewness (taking your mean and starting- and end-points to determine the distribution). This gives

skewness of data: 0.7071062587209218
skewness of distribution: 53.32916979819496