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Included method to generate beta dist for f_inf

Luis Aleixo requested to merge f_inf_beta_dist into master

Control variable: use_f_inf_beta_dist, default value is False.

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Example with Breathing:

Before:

<<<<<<<<<<< Breathing model statistics >>>>>>>>>>>
MEAN of ER = 37.63271648725738
MEAN of log ER = -0.7371916316107616
SD of ER = 166.02798389727252
SD of log ER = 1.83937110747628
Median of ER = 0.19952079549488433

After:

<<<<<<<<<<< Breathing model statistics >>>>>>>>>>>
MEAN of ER = 0.3653022494812487
MEAN of log ER = -2.7208944676176845
SD of ER = 1.6136395771160308
SD of log ER = 1.8260566475258184
Median of ER = 0.002070448950140658

Example with Speaking:

Before:

<<<<<<<<<<< Speaking model statistics >>>>>>>>>>>
MEAN of ER = 3889.4369193802677
MEAN of log ER = 1.2760255033601542
SD of ER = 17260.271330297848
SD of log ER = 1.8400108331118465
Median of ER = 20.73087759775555

After:

<<<<<<<<<<< Speaking model statistics >>>>>>>>>>>
MEAN of ER = 36.00410092395356
MEAN of log ER = -0.7244939857748114
SD of ER = 158.17097278516036
SD of log ER = 1.8258123136399595
Median of ER = 0.20510464586294302

Example with Shouting:

Before:

<<<<<<<<<<< Shouting model statistics >>>>>>>>>>>
MEAN of ER = 19310.84012342309
MEAN of log ER = 1.9709808900257666
SD of ER = 85693.67698836152
SD of log ER = 1.8410863844411303
Median of ER = 102.4466565942783

After:

<<<<<<<<<<< Shouting model statistics >>>>>>>>>>>
MEAN of ER = 188.40508260530558
MEAN of log ER = -0.005426711406534044
SD of ER = 827.7241721728336
SD of log ER = 1.8268447366976621
Median of ER = 1.0761273159525877

Source for beta distribution:

https://www.sciencedirect.com/science/article/pii/S2950362024000225

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@andrejh added you as a reviewer to be aware of the development. Ready to merge for testing.

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