Fitting empirical distribution to theoretical ones with Scipy (Python)?

Question

INTRODUCTION: I have a list of more than 30,000 integer values ranging from 0 to 47, inclusive, e.g.[0,0,0,0,..,1,1,1,1,...,2,2,2,2,...,47,47,47,...]<

Answer 1

Try the distfit library.

pip install distfit

# Create 1000 random integers, value between [0-50]
X = np.random.randint(0, 50,1000)

# Retrieve P-value for y
y = [0,10,45,55,100]

# From the distfit library import the class distfit
from distfit import distfit

# Initialize.
# Set any properties here, such as alpha.
# The smoothing can be of use when working with integers. Otherwise your histogram
# may be jumping up-and-down, and getting the correct fit may be harder.
dist = distfit(alpha=0.05, smooth=10)

# Search for best theoretical fit on your empirical data
dist.fit_transform(X)

> [distfit] >fit..
> [distfit] >transform..
> [distfit] >[norm      ] [RSS: 0.0037894] [loc=23.535 scale=14.450] 
> [distfit] >[expon     ] [RSS: 0.0055534] [loc=0.000 scale=23.535] 
> [distfit] >[pareto    ] [RSS: 0.0056828] [loc=-384473077.778 scale=384473077.778] 
> [distfit] >[dweibull  ] [RSS: 0.0038202] [loc=24.535 scale=13.936] 
> [distfit] >[t         ] [RSS: 0.0037896] [loc=23.535 scale=14.450] 
> [distfit] >[genextreme] [RSS: 0.0036185] [loc=18.890 scale=14.506] 
> [distfit] >[gamma     ] [RSS: 0.0037600] [loc=-175.505 scale=1.044] 
> [distfit] >[lognorm   ] [RSS: 0.0642364] [loc=-0.000 scale=1.802] 
> [distfit] >[beta      ] [RSS: 0.0021885] [loc=-3.981 scale=52.981] 
> [distfit] >[uniform   ] [RSS: 0.0012349] [loc=0.000 scale=49.000] 

# Best fitted model
best_distr = dist.model
print(best_distr)

# Uniform shows best fit, with 95% CII (confidence intervals), and all other parameters
> {'distr': ,
>  'params': (0.0, 49.0),
>  'name': 'uniform',
>  'RSS': 0.0012349021241149533,
>  'loc': 0.0,
>  'scale': 49.0,
>  'arg': (),
>  'CII_min_alpha': 2.45,
>  'CII_max_alpha': 46.55}

# Ranking distributions
dist.summary

# Plot the summary of fitted distributions
dist.plot_summary()

# Make prediction on new datapoints based on the fit
dist.predict(y)

# Retrieve your pvalues with 
dist.y_pred
# array(['down', 'none', 'none', 'up', 'up'], dtype='

Note that in this case, all points will be significant because of the uniform distribution. You can filter with the dist.y_pred if required.