phitter 0.7

Find the best probability distribution for your dataset

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

data: list[int | float] = [...]

phitter_cont = phitter.PHITTER(data)
phitter_cont.fit()

Full continuous implementation

import phitter

data: list[int | float] = [...]

phitter_cont = 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"],
)
phitter_cont.fit(n_workers=6)

Full discrete implementation

import phitter

data: list[int | float] = [...]

phitter_disc = phitter.PHITTER(
    data=data,
    fit_type="discrete",
    confidence_level=0.95,
    minimum_sse=1e-2,
    distributions_to_fit=["binomial", "geometric"],
)
phitter_disc.fit(n_workers=2)

Phitter: properties and methods

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

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

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

Histogram Plot

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

phitter_cont.plot_histogram()

Histogram PDF Dsitributions Plot

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

phitter_cont.plot_histogram_distributions()

Histogram PDF Dsitribution Plot

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

phitter_cont.plot_distribution("beta")

ECDF Plot

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

phitter_cont.plot_ecdf()

ECDF Distribution Plot

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

phitter_cont.plot_ecdf_distribution("beta")

QQ Plot

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

phitter_cont.qq_plot("beta")

QQ - Regression Plot

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

phitter_cont.qq_plot_regression("beta")

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:generalized_extreme_value	📊generalized_extreme_value.xlsx	🌐gs:generalized_extreme_value
generalized_gamma	▶️phitter:generalized_gamma	📊generalized_gamma.xlsx	🌐gs:generalized_gamma
generalized_gamma_4p	▶️phitter:generalized_gamma_4p	📊generalized_gamma_4p.xlsx	🌐gs:generalized_gamma_4p
generalized_logistic	▶️phitter:generalized_logistic	📊generalized_logistic.xlsx	🌐gs:generalized_logistic
generalized_normal	▶️phitter:generalized_normal	📊generalized_normal.xlsx	🌐gs:generalized_normal
generalized_pareto	▶️phitter:generalized_pareto	📊generalized_pareto.xlsx	🌐gs:generalized_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!