Description:

phitter 0.7.1

Phitter analyzes datasets and determines the best analytical probability distributions that represent them. Phitter studies over 80 probability distributions, both continuous and discrete, 3 goodness-of-fit tests, and interactive visualizations. For each selected probability distribution, a standard modeling guide is provided along with spreadsheets that detail the methodology for using the chosen distribution in data science, operations research, and artificial intelligence.


This repository contains the implementation of the python library and the kernel of Phitter Web

Installation
Requirements
python: >=3.9

PyPI
pip install phitter

Usage
Notebook's Tutorials



Tutorial
Notebooks




Fit Continuous



Fit Discrete



Fit Accelerate [Sample>100K]



Fit Specific Disribution



Working Distribution




General
import phitter

## Define your dataset
data: list[int | float] = [...]

## Make a continuous fit using Phitter
phi = phitter.PHITTER(data)
phi.fit()

Full continuous implementation
import phitter

## Define your dataset
data: list[int | float] = [...]

## Make a continuous fit using Phitter
phi = phitter.PHITTER(
data=data,
fit_type="continuous",
num_bins=15,
confidence_level=0.95,
minimum_sse=1e-2,
distributions_to_fit=["beta", "normal", "fatigue_life", "triangular"],
)
phi.fit(n_workers=6)

Full discrete implementation
import phitter

## Define your dataset
data: list[int | float] = [...]

## Make a discrete fit using Phitter
phi = phitter.PHITTER(
data=data,
fit_type="discrete",
confidence_level=0.95,
minimum_sse=1e-2,
distributions_to_fit=["binomial", "geometric"],
)
phi.fit(n_workers=2)

Phitter: properties and methods
import phitter

## Define your dataset
data: list[int | float] = [...]

## Make a fit using Phitter
phi = phitter.PHITTER(data)
phi.fit(n_workers=2)

## Global methods and properties
phi.summarize(k: int) -> pandas.DataFrame
phi.summarize_info(k: int) -> pandas.DataFrame
phi.best_distribution -> dict
phi.sorted_distributions_sse -> dict
phi.not_rejected_distributions -> dict
phi.df_sorted_distributions_sse -> pandas.DataFrame
phi.df_not_rejected_distributions -> pandas.DataFrame

## Specific distribution methods and properties
phi.get_parameters(id_distribution: str) -> dict
phi.get_test_chi_square(id_distribution: str) -> dict
phi.get_test_kolmmogorov_smirnov(id_distribution: str) -> dict
phi.get_test_anderson_darling(id_distribution: str) -> dict
phi.get_sse(id_distribution: str) -> float
phi.get_n_test_passed(id_distribution: str) -> int
phi.get_n_test_null(id_distribution: str) -> int

Histogram Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.plot_histogram()


Histogram PDF Dsitributions Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.plot_histogram_distributions()


Histogram PDF Dsitribution Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.plot_distribution("beta")


ECDF Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.plot_ecdf()


ECDF Distribution Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.plot_ecdf_distribution("beta")


QQ Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.qq_plot("beta")


QQ - Regression Plot
import phitter
data: list[int | float] = [...]
phi = phitter.PHITTER(data)
phi.fit()

phi.qq_plot_regression("beta")


Working with distributions: Methods and properties
import phitter

distribution = phitter.continuous.BETA({"alpha": 5, "beta": 3, "A": 200, "B": 1000})

## CDF, PDF, PPF, PMF receive float or numpy.ndarray. For discrete distributions PMF instead of PDF. Parameters notation are in description of ditribution
distribution.cdf(752) # -> 0.6242831129533498
distribution.pdf(388) # -> 0.0002342575686629883
distribution.ppf(0.623) # -> 751.5512889417921
distribution.sample(2) # -> [550.800114 514.85410326]

## STATS
distribution.mean # -> 700.0
distribution.variance # -> 16666.666666666668
distribution.standard_deviation # -> 129.09944487358058
distribution.skewness # -> -0.3098386676965934
distribution.kurtosis # -> 2.5854545454545454
distribution.median # -> 708.707130841534
distribution.mode # -> 733.3333333333333

Continuous Distributions
1. PDF File Documentation Continuous Distributions
2. Resources Continuous Distributions



Distribution
Phitter Playground
Excel File
Google Sheets Files




alpha
▶️phitter:alpha
📊alpha.xlsx
🌐gs:alpha


arcsine
▶️phitter:arcsine
📊arcsine.xlsx
🌐gs:arcsine


argus
▶️phitter:argus
📊argus.xlsx
🌐gs:argus


beta
▶️phitter:beta
📊beta.xlsx
🌐gs:beta


beta_prime
▶️phitter:beta_prime
📊beta_prime.xlsx
🌐gs:beta_prime


beta_prime_4p
▶️phitter:beta_prime_4p
📊beta_prime_4p.xlsx
🌐gs:beta_prime_4p


bradford
▶️phitter:bradford
📊bradford.xlsx
🌐gs:bradford


burr
▶️phitter:burr
📊burr.xlsx
🌐gs:burr


burr_4p
▶️phitter:burr_4p
📊burr_4p.xlsx
🌐gs:burr_4p


cauchy
▶️phitter:cauchy
📊cauchy.xlsx
🌐gs:cauchy


chi_square
▶️phitter:chi_square
📊chi_square.xlsx
🌐gs:chi_square


chi_square_3p
▶️phitter:chi_square_3p
📊chi_square_3p.xlsx
🌐gs:chi_square_3p


dagum
▶️phitter:dagum
📊dagum.xlsx
🌐gs:dagum


dagum_4p
▶️phitter:dagum_4p
📊dagum_4p.xlsx
🌐gs:dagum_4p


erlang
▶️phitter:erlang
📊erlang.xlsx
🌐gs:erlang


erlang_3p
▶️phitter:erlang_3p
📊erlang_3p.xlsx
🌐gs:erlang_3p


error_function
▶️phitter:error_function
📊error_function.xlsx
🌐gs:error_function


exponential
▶️phitter:exponential
📊exponential.xlsx
🌐gs:exponential


exponential_2p
▶️phitter:exponential_2p
📊exponential_2p.xlsx
🌐gs:exponential_2p


f
▶️phitter:f
📊f.xlsx
🌐gs:f


f_4p
▶️phitter:f_4p
📊f_4p.xlsx
🌐gs:f_4p


fatigue_life
▶️phitter:fatigue_life
📊fatigue_life.xlsx
🌐gs:fatigue_life


folded_normal
▶️phitter:folded_normal
📊folded_normal.xlsx
🌐gs:folded_normal


frechet
▶️phitter:frechet
📊frechet.xlsx
🌐gs:frechet


gamma
▶️phitter:gamma
📊gamma.xlsx
🌐gs:gamma


gamma_3p
▶️phitter:gamma_3p
📊gamma_3p.xlsx
🌐gs:gamma_3p


generalized_extreme_value
▶️phitter:gen_extreme_value
📊gen_extreme_value.xlsx
🌐gs:gen_extreme_value


generalized_gamma
▶️phitter:gen_gamma
📊gen_gamma.xlsx
🌐gs:gen_gamma


generalized_gamma_4p
▶️phitter:gen_gamma_4p
📊gen_gamma_4p.xlsx
🌐gs:gen_gamma_4p


generalized_logistic
▶️phitter:gen_logistic
📊gen_logistic.xlsx
🌐gs:gen_logistic


generalized_normal
▶️phitter:gen_normal
📊gen_normal.xlsx
🌐gs:gen_normal


generalized_pareto
▶️phitter:gen_pareto
📊gen_pareto.xlsx
🌐gs:gen_pareto


gibrat
▶️phitter:gibrat
📊gibrat.xlsx
🌐gs:gibrat


gumbel_left
▶️phitter:gumbel_left
📊gumbel_left.xlsx
🌐gs:gumbel_left


gumbel_right
▶️phitter:gumbel_right
📊gumbel_right.xlsx
🌐gs:gumbel_right


half_normal
▶️phitter:half_normal
📊half_normal.xlsx
🌐gs:half_normal


hyperbolic_secant
▶️phitter:hyperbolic_secant
📊hyperbolic_secant.xlsx
🌐gs:hyperbolic_secant


inverse_gamma
▶️phitter:inverse_gamma
📊inverse_gamma.xlsx
🌐gs:inverse_gamma


inverse_gamma_3p
▶️phitter:inverse_gamma_3p
📊inverse_gamma_3p.xlsx
🌐gs:inverse_gamma_3p


inverse_gaussian
▶️phitter:inverse_gaussian
📊inverse_gaussian.xlsx
🌐gs:inverse_gaussian


inverse_gaussian_3p
▶️phitter:inverse_gaussian_3p
📊inverse_gaussian_3p.xlsx
🌐gs:inverse_gaussian_3p


johnson_sb
▶️phitter:johnson_sb
📊johnson_sb.xlsx
🌐gs:johnson_sb


johnson_su
▶️phitter:johnson_su
📊johnson_su.xlsx
🌐gs:johnson_su


kumaraswamy
▶️phitter:kumaraswamy
📊kumaraswamy.xlsx
🌐gs:kumaraswamy


laplace
▶️phitter:laplace
📊laplace.xlsx
🌐gs:laplace


levy
▶️phitter:levy
📊levy.xlsx
🌐gs:levy


loggamma
▶️phitter:loggamma
📊loggamma.xlsx
🌐gs:loggamma


logistic
▶️phitter:logistic
📊logistic.xlsx
🌐gs:logistic


loglogistic
▶️phitter:loglogistic
📊loglogistic.xlsx
🌐gs:loglogistic


loglogistic_3p
▶️phitter:loglogistic_3p
📊loglogistic_3p.xlsx
🌐gs:loglogistic_3p


lognormal
▶️phitter:lognormal
📊lognormal.xlsx
🌐gs:lognormal


maxwell
▶️phitter:maxwell
📊maxwell.xlsx
🌐gs:maxwell


moyal
▶️phitter:moyal
📊moyal.xlsx
🌐gs:moyal


nakagami
▶️phitter:nakagami
📊nakagami.xlsx
🌐gs:nakagami


non_central_chi_square
▶️phitter:non_central_chi_square
📊non_central_chi_square.xlsx
🌐gs:non_central_chi_square


non_central_f
▶️phitter:non_central_f
📊non_central_f.xlsx
🌐gs:non_central_f


non_central_t_student
▶️phitter:non_central_t_student
📊non_central_t_student.xlsx
🌐gs:non_central_t_student


normal
▶️phitter:normal
📊normal.xlsx
🌐gs:normal


pareto_first_kind
▶️phitter:pareto_first_kind
📊pareto_first_kind.xlsx
🌐gs:pareto_first_kind


pareto_second_kind
▶️phitter:pareto_second_kind
📊pareto_second_kind.xlsx
🌐gs:pareto_second_kind


pert
▶️phitter:pert
📊pert.xlsx
🌐gs:pert


power_function
▶️phitter:power_function
📊power_function.xlsx
🌐gs:power_function


rayleigh
▶️phitter:rayleigh
📊rayleigh.xlsx
🌐gs:rayleigh


reciprocal
▶️phitter:reciprocal
📊reciprocal.xlsx
🌐gs:reciprocal


rice
▶️phitter:rice
📊rice.xlsx
🌐gs:rice


semicircular
▶️phitter:semicircular
📊semicircular.xlsx
🌐gs:semicircular


t_student
▶️phitter:t_student
📊t_student.xlsx
🌐gs:t_student


t_student_3p
▶️phitter:t_student_3p
📊t_student_3p.xlsx
🌐gs:t_student_3p


trapezoidal
▶️phitter:trapezoidal
📊trapezoidal.xlsx
🌐gs:trapezoidal


triangular
▶️phitter:triangular
📊triangular.xlsx
🌐gs:triangular


uniform
▶️phitter:uniform
📊uniform.xlsx
🌐gs:uniform


weibull
▶️phitter:weibull
📊weibull.xlsx
🌐gs:weibull


weibull_3p
▶️phitter:weibull_3p
📊weibull_3p.xlsx
🌐gs:weibull_3p



Discrete Distributions
1. PDF File Documentation Discrete Distributions
2. Resources Discrete Distributions



Distribution
Phitter Playground
Excel File
Google Sheets Files




bernoulli
▶️phitter:bernoulli
📊bernoulli.xlsx
🌐gs:bernoulli


binomial
▶️phitter:binomial
📊binomial.xlsx
🌐gs:binomial


geometric
▶️phitter:geometric
📊geometric.xlsx
🌐gs:geometric


hypergeometric
▶️phitter:hypergeometric
📊hypergeometric.xlsx
🌐gs:hypergeometric


logarithmic
▶️phitter:logarithmic
📊logarithmic.xlsx
🌐gs:logarithmic


negative_binomial
▶️phitter:negative_binomial
📊negative_binomial.xlsx
🌐gs:negative_binomial


poisson
▶️phitter:poisson
📊poisson.xlsx
🌐gs:poisson


uniform
▶️phitter:uniform
📊uniform.xlsx
🌐gs:uniform



Benchmarks
Fit time continuous distributions



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



Estimation time parameters discrete distributions



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



Estimation time parameters continuous distributions



Distribution / Sample Size
1K
10K
100K
500K
1M
10M




alpha
0.3345
0.4625
2.5933
18.3856
39.6533
362.2951


arcsine
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


argus
0.0559
0.2050
2.2472
13.3928
41.5198
362.2472


beta
0.1880
0.1790
0.1940
0.2110
0.1800
0.3134


beta_prime
0.1766
0.7506
7.6039
40.4264
85.0677
812.1323


beta_prime_4p
0.0720
0.3630
3.9478
20.2703
40.2709
413.5239


bradford
0.0110
0.0000
0.0000
0.0000
0.0000
0.0010


burr
0.0733
0.6931
5.5425
36.7684
79.8269
668.2016


burr_4p
0.1552
0.7981
8.4716
44.4549
87.7292
858.0035


cauchy
0.0090
0.0160
0.1581
1.1052
2.1090
21.5244


chi_square
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


chi_square_3p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


dagum
0.3381
0.8278
9.6907
45.5855
98.6691
917.6713


dagum_4p
0.3646
1.3307
13.3437
70.9462
140.9371
1396.3368


erlang
0.0010
0.0000
0.0000
0.0000
0.0000
0.0000


erlang_3p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


error_function
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


exponential
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


exponential_2p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


f
0.0592
0.2948
2.6920
18.9458
29.9547
402.2248


fatigue_life
0.0352
0.1101
1.7085
9.0090
20.4702
186.9631


folded_normal
0.0020
0.0020
0.0020
0.0022
0.0033
0.0040


frechet
0.1313
0.4359
5.7031
39.4202
43.2469
671.3343


f_4p
0.3269
0.7517
0.6183
0.6037
0.5809
0.2073


gamma
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


gamma_3p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


generalized_extreme_value
0.0833
0.2054
2.0337
10.3301
22.1340
243.3120


generalized_gamma
0.0298
0.0178
0.0227
0.0236
0.0170
0.0241


generalized_gamma_4p
0.0371
0.0116
0.0732
0.0725
0.0707
0.0730


generalized_logistic
0.1040
0.1073
0.1037
0.0819
0.0989
0.0836


generalized_normal
0.0154
0.0736
0.7367
2.4831
5.9752
55.2417


generalized_pareto
0.3189
0.8978
8.9370
51.3813
101.6832
1015.2933


gibrat
0.0328
0.0432
0.4287
2.7159
5.5721
54.1702


gumbel_left
0.0000
0.0000
0.0000
0.0000
0.0010
0.0010


gumbel_right
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


half_normal
0.0010
0.0000
0.0000
0.0010
0.0000
0.0000


hyperbolic_secant
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


inverse_gamma
0.0308
0.0632
0.7233
5.0127
10.7885
99.1316


inverse_gamma_3p
0.0787
0.1472
1.6513
11.1161
23.4587
227.6125


inverse_gaussian
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


inverse_gaussian_3p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


johnson_sb
0.2966
0.7466
4.0707
40.2028
56.2130
728.2447


johnson_su
0.0070
0.0010
0.0010
0.0143
0.0010
0.0010


kumaraswamy
0.0164
0.0120
0.0130
0.0123
0.0125
0.0150


laplace
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


levy
0.0100
0.0314
0.2296
1.1365
2.7211
26.4966


loggamma
0.0085
0.0050
0.0050
0.0070
0.0062
0.0080


logistic
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


loglogistic
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


loglogistic_3p
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


lognormal
0.0000
0.0000
0.0000
0.0000
0.0010
0.0000


maxwell
0.0000
0.0000
0.0000
0.0000
0.0000
0.0010


moyal
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


nakagami
0.0000
0.0030
0.0213
0.1215
0.2649
2.2457


non_central_chi_square
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


non_central_f
0.0190
0.0182
0.0210
0.0192
0.0190
0.0200


non_central_t_student
0.0874
0.0822
0.0862
0.1314
0.2516
0.1781


normal
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


pareto_first_kind
0.0010
0.0030
0.0390
0.2494
0.5226
5.5246


pareto_second_kind
0.0643
0.1522
1.1722
10.9871
23.6534
201.1626


pert
0.0052
0.0030
0.0030
0.0040
0.0040
0.0092


power_function
0.0075
0.0040
0.0040
0.0030
0.0040
0.0040


rayleigh
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


reciprocal
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


rice
0.0182
0.0030
0.0040
0.0060
0.0030
0.0050


semicircular
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


trapezoidal
0.0083
0.0072
0.0073
0.0060
0.0070
0.0060


triangular
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


t_student
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


t_student_3p
0.3892
1.1860
11.2759
71.1156
143.1939
1409.8578


uniform
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


weibull
0.0010
0.0000
0.0000
0.0000
0.0010
0.0010


weibull_3p
0.0061
0.0040
0.0030
0.0040
0.0050
0.0050



Estimation time parameters discrete distributions



Distribution / Sample Size
1K
10K
100K
500K
1M
10M




bernoulli
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


binomial
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


geometric
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


hypergeometric
0.0773
0.0061
0.0030
0.0020
0.0030
0.0051


logarithmic
0.0210
0.0035
0.0171
0.0050
0.0030
0.0756


negative_binomial
0.0293
0.0000
0.0000
0.0000
0.0000
0.0000


poisson
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000


uniform
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000



Contribution
If you would like to contribute to the Phitter project, please create a pull request with your proposed changes or enhancements. All contributions are welcome!

License

For personal and professional use. You cannot resell or redistribute these repositories in their original state.

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