Workers

The fitting procedure for continuous distributions is performed by invoking the .fit() method. This method provides a parameter n_workers (int, optional), which designates the number of parallel processes employed during the fitting procedure. By default, this parameter is set to 1. An example usage is illustrated below:

phi.fit(n_workers=4)

Although parallelization can reduce overall processing time, the relationship between sample size, number of workers, and execution speed is non-trivial. Excessive parallelization may introduce significant overhead and resource contention, causing longer run times in certain scenarios.

Benchmarks: Standard Google Colab Instance

Continuous Fit Time: Sample Size vs. Workers

Sample Size / Workers	1	2	6	10	20
1K	8.2981	7.1242	8.9667	9.9287	16.2246
10K	20.8711	14.2647	10.5612	11.6004	17.8562
100K	152.6296	97.2359	57.7310	51.6182	53.2313
500K	914.9291	640.8153	370.0323	267.4597	257.7534
1M	1580.8501	972.3985	573.5429	496.5569	425.7809

Analysis (Continuous):

• For smaller sample sizes (e.g., 1K), the use of two workers yields a moderate improvement over a single worker, whereas a higher number of workers (6, 10, and 20) actually results in increased computation time. This behavior arises from synchronization overhead and resource competition.
• With larger sample sizes (e.g., 500K and 1M), adding more workers generally decreases computation time, yet the benefit can plateau or even revert if the overhead becomes too large.

Discrete Fit Time: Sample Size vs. Workers

Sample Size / Workers	1	2	4
1K	0.1688	2.6402	2.8719
10K	0.4462	2.4452	3.0471
100K	4.5598	6.3246	7.5869
500K	19.0172	21.8047	19.8420
1M	39.8065	29.8360	30.2334

Analysis (Discrete):

• In the discrete case, employing multiple workers for smaller samples frequently leads to significantly longer times, indicating that overhead can outweigh the benefits of parallelization.
• When the sample size is large (e.g., 1M), increased parallelization may reduce time; however, certain configurations still display regressions in performance, likely due to factors such as inter-process communication overhead.

Conclusion:
The optimal choice of n_workers depends on the interplay among sample size, distribution type, and computational resources. Although using more workers can be advantageous in many situations—particularly for extensive datasets—there are clear instances where excessive parallelization diminishes performance. It is therefore advisable to test multiple worker configurations to identify the most efficient setting for a given context.