Find the best probability distribution for your dataset and simulate processes and queues
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.
Additionally, Phitter enables advanced process simulations, allowing to model and visualize key performance metrics such as minimum observation times. It facilitates the simulation of queuing systems with configurable parameters, including the number of servers, system capacity, maximum population size, and service discipline. Supported queuing models encompass FIFO, LIFO and PBS, ensuring adaptability to various operational and research applications.
This repository contains the implementation of the python library and the kernel of Phitter Web
Find the complete Phitter documentation here.
python: >=3.9
pip install phitter
| Tutorial | Notebooks |
|---|---|
| Fit Continuous |  |
| Fit Discrete | |
| Fit Accelerate [Sample>100K] | |
| Fit Specific Distribution | |
| Working Distribution | |
| Tutorial | Notebooks |
|---|---|
| Process Simulation | |
| Own Distribution | |
| Queue Simulation First-In-First-Out (FIFO) | |
| Queue Simulation Last-In-First-Out (LIFO) | |
| Queue Simulation Priority-Based Service (PBS) | |
import phitter
## Define your dataset
data: list[int | float] = [...]
## Make a continuous fit using Phitter
phi = phitter.Phitter(data=data)
phi.fit()
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)
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)
import phitter
## Define your dataset
data: list[int | float] = [...]
## Make a fit using Phitter
phi = phitter.Phitter(data=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
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.plot_histogram()
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.plot_histogram_distributions()
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.plot_distribution("beta")
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.plot_ecdf()
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.plot_ecdf_distribution("beta")
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.qq_plot("beta")
import phitter
data: list[int | float] = [...]
phi = phitter.Phitter(data=data)
phi.fit()
phi.qq_plot_regression("beta")
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
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
This will help you to understand your processes. To use it, run the following line
from phitter import simulation
# Create a simulation process instance
simulation = simulation.ProcessSimulation()
There are two ways to add processes to your simulation instance:
# Add a new process without preceding process
simulation.add_process(
prob_distribution="normal",
parameters={"mu": 5, "sigma": 2},
process_id="first_process",
number_of_products=10,
number_of_servers=3,
new_branch=True,
)
# Add a new process with preceding process
simulation.add_process(
prob_distribution="exponential",
parameters={"lambda": 4},
process_id="second_process",
previous_ids=["first_process"],
)
The order in which you add each process matters. You can add as many processes as you need.
# Add a new process without preceding process
simulation.add_process(
prob_distribution="normal",
parameters={"mu": 5, "sigma": 2},
process_id="first_process",
number_of_products=10,
number_of_servers=3,
new_branch=True,
)
# Add a new process with preceding process
simulation.add_process(
prob_distribution="exponential",
parameters={"lambda": 4},
process_id="second_process",
previous_ids=["first_process"],
)
# Add a new process with preceding process
simulation.add_process(
prob_distribution="gamma",
parameters={"alpha": 15, "beta": 3},
process_id="third_process",
previous_ids=["first_process"],
)
# Add a new process without preceding process
simulation.add_process(
prob_distribution="exponential",
parameters={"lambda": 4.3},
process_id="fourth_process",
new_branch=True,
)
# Add a new process with preceding process
simulation.add_process(
prob_distribution="beta",
parameters={"alpha": 1, "beta": 1, "A": 2, "B": 3},
process_id="fifth_process",
previous_ids=["second_process", "fourth_process"],
)
# Add a new process with preceding process
simulation.add_process(
prob_distribution="normal",
parameters={"mu": 15, "sigma": 2},
process_id="sixth_process",
previous_ids=["third_process", "fifth_process"],
)
You can visualize your processes to see if what you're trying to simulate is your actual process.
# Graph your process
simulation.process_graph()
You can simulate and have different simulation time values or you can create a confidence interval for your process
Simulate several scenarios of your complete process
# Run Simulation
simulation.run(number_of_simulations=100)
# After run
simulation: pandas.Dataframe
If you want to review average time and standard deviation by stage run this line of code
# Review simulation metrics
simulation.simulation_metrics() -> pandas.Dataframe
If you want to have a confidence interval for the simulation metrics, run the following line of code
# Confidence interval for Simulation metrics
simulation.run_confidence_interval(
confidence_level=0.99,
number_of_simulations=100,
replications=10,
) -> pandas.Dataframe
If you need to simulate queues run the following code:
from phitter import simulation
# Create a simulation process instance
simulation = simulation.QueueingSimulation(
a="exponential",
a_parameters={"lambda": 5},
s="exponential",
s_parameters={"lambda": 20},
c=3,
)
In this case we are going to simulate a (arrivals) with exponential distribution and s (service) as exponential distribution with c equals to 3 different servers.
By default Maximum Capacity k is infinity, total population n is infinity and the queue discipline d is FIFO. As we are not selecting d equals to "PBS" we don't have any information to add for pbs_distribution nor pbs_parameters
If you want to have the simulation results
# Run simulation
simulation.run(simulation_time = 2000)
If you want to see some metrics and probabilities from this simulation you should use::
# Calculate metrics
simulation.metrics_summary() -> pandas.Dataframe
# Calculate probabilities
simulation.number_probability_summary() -> pandas.Dataframe
If you want to have a confidence interval for your metrics and probabilities you should run the following line
# Calculate confidence interval for metrics and probabilities
probabilities, metrics = simulation.confidence_interval_metrics(
simulation_time=2000,
confidence_level=0.99,
replications=10,
)
probabilities -> pandas.Dataframe
metrics -> pandas.Dataframe
All contributions and collaborations are welcome!
For bugs, feature requests, and clear suggestions for improvement please open an issue.
If you have built something upon Phitter-Kernel that would be useful to others, or can address an open issue, please fork the repository and open a pull request.
FAQs
Find the best probability distribution for your dataset and simulate processes and queues
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