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If you’re working with Python and need to fit probability distributions to your data, Phitter is a powerful library that can help. However, its documentation leaves some questions unanswered, particularly about how it handles different types of data and distributions. This article will show you how to use Phitter effectively and avoid common pitfalls.

Installation and Package Status

Phitter can be easily installed using pip:

pip install phitter

The current version (1.0.0) was released in November 2024 and thus is a relatively new package that’s actively being developed. The latest download offers over 80 probability distributions and comprehensive tools for data analysis. However, as with any new software, you can expect regular updates and improvements. Be sure to check the official documentation for the latest features and best practices.

What You Need to Know About Phitter

1. No Automatic Type Detection: Phitter won’t automatically determine whether your data should be modeled with continuous or discrete distributions.
2. User-Driven Decision: You need to explicitly choose between continuous and discrete distribution families.
3. Default Behavior: Without specification, Phitter defaults to continuous distributions.
4. Data Type Independence: Python data types (int vs float) don’t influence distribution selection.

Distribution Fitting in Practice: Three Examples

Example 1: Default Behavior with Count Data

import phitter
import numpy as np

# Example 1: Default Behavior
count_data = [1, 2, 2, 3, 3, 3, 4, 4, 5]  # Integer data
phi_default = phitter.PHITTER(data=count_data)
phi_default.fit()

print("Default fitting (no fit_type specified):")
print(f"Data Type: {type(count_data[0])}") 
print(f"Best distribution: {phi_default.best_distribution}")

Output:

Default fitting (no fit_type specified):
Data Type: <class 'int'>
Best distribution: {'id': 'gumbel_left', 'parameters': {'mu': 3.5512003584032428, 'sigma': 0.9549296596080912}}

What’s happening here? Even though we’re using integer count data, Phitter defaults to fitting continuous distributions. In this case, it selected a Gumbel left distribution, which might not be the most appropriate choice for count data.

Example 2: Proper Discrete Fitting

# Example 2: Explicit Discrete Fitting
phi_discrete = phitter.PHITTER(
    data=count_data,
    fit_type="discrete",
    confidence_level=0.95
)
phi_discrete.fit()
print("\nDiscrete fitting:")
print(f"Best distribution: {phi_discrete.best_distribution}")

Output:

Discrete fitting:
Best distribution: {'id': 'binomial', 'parameters': {'n': 6, 'p': 0.5}}

What’s happening here? By explicitly specifying fit_type=”discrete”, we get a binomial distribution fit, which is more appropriate for count data. Notice how the parameters (n and p) have clear interpretations in the context of count data.

Example 3: Comparing Continuous and Discrete Distributions

import phitter
import numpy as np

# Example 3: Comparing Continuous and Discrete Fitting
# Generate some sample data
np.random.seed(42)
continuous_data = np.random.normal(loc=10, scale=2, size=1000)  # Measurements
count_data = np.random.poisson(lam=5, size=1000)  # Count data

# Fit continuous data
phi_continuous = phitter.PHITTER(
    data=continuous_data,
    fit_type="continuous",
    confidence_level=0.95
)
phi_continuous.fit()

# Fit count data
phi_discrete = phitter.PHITTER(
    data=count_data,
    fit_type="discrete",
    confidence_level=0.95
)
phi_discrete.fit()

# Compare results
print("Continuous data fitting:")
print(f"Best distribution: {phi_continuous.best_distribution}")
print("\nCount data fitting:")
print(f"Best distribution: {phi_discrete.best_distribution}")

# Plot the fits
phi_continuous.plot_histogram_distributions()
phi_discrete.plot_histogram_distributions()

Output:

Continuous data fitting:
Best distribution: {'id': 'gamma_3p', 'parameters': {'alpha': 292.3234930850778, 'loc': -23.44556686790844, 'beta': 0.11454512473894064}}

Count data fitting:
Best distribution: {'id': 'hypergeometric', 'parameters': {'N': 5364, 'K': 163, 'n': 164}}

Image By Author

Understanding the Continuous Fit: The histogram shows how multiple continuous distributions (gamma_3p, inverse_gaussian_3p, beta, etc.) fit the data. The best fit (gamma_3p) is shown in blue, with other candidates in different colors. The smooth curves overlaying the histogram indicate how well each distribution captures the data’s shape.

Image By Author

Understanding the Discrete Fit: This histogram shows discrete distribution fits (hypergeometric, binomial, poisson, etc.). Notice how the fitted distributions follow the step-like pattern typical of discrete data, rather than the smooth curves seen in continuous fits.

How to Choose the Right Approach

1. For Discrete Fitting (fit_type=”discrete”), use when your data:
   • Represents counts (number of events, occurrences)
   • Can only take whole number values
   • Has a finite, countable set of possible values
   • Examples: Customer arrivals, defects per unit, binary outcomes
2. For Continuous Fitting (fit_type=”continuous”), use when your data:
   • Represents measurements on a continuous scale
   • Can theoretically take any value within a range
   • Has high precision or decimal values
   • Examples: Time durations, temperatures, distances

Best Practices and Tips

1. Examine Your Data First: Before fitting, look at:
   • The nature of your measurements
   • The range and precision of values
   • Whether values are naturally discrete or continuous
2. Validate Your Choice:
   • Use Phitter’s visualization tools to assess fit quality
   • Compare goodness-of-fit metrics
   • Consider the practical interpretation of the fitted parameters
3. When in Doubt:
   • Try both approaches and compare the results
   • Consider your data’s real-world meaning
   • Look at the interpretability of the fitted parameters

Conclusion

While Phitter defaults to continuous distributions, understanding how to choose between continuous and discrete fitting is essential for accurate analysis. The key is to let your data’s inherent characteristics and your analytical objectives drive the decision, rather than relying solely on automatic detection or the underlying Python data types. For further clarification on the differences between discrete and continuous variables, consider exploring our detailed guide entitled, “Understanding Variable Types in Statistics: Discrete vs Continuous.“