Distribution Parameter Reference

This guide documents the parameter naming conventions used across all distribution classes in quActuary.

Important

As of version 0.2.0, all distributions use loc for location parameters (not location or threshold). This was standardized to ensure consistency across the API.

Overview

quActuary uses consistent parameter naming conventions across its distribution classes:

  • Location parameter: Always use loc

  • Scale parameter: Always use scale

  • Shape parameters: Vary by distribution type but follow statistical conventions

Parameter Naming by Distribution Type

Frequency Distributions

Frequency Distribution Parameters

Distribution

Parameters

Binomial

n (number of trials), p (probability of success)

DeterministicFrequency

value (fixed frequency value)

DiscreteUniformFrequency

low (minimum value), high (maximum value)

EmpiricalFrequency

pmf_values (dictionary of value: probability pairs)

Geometric

p (probability of success)

Hypergeometric

M (population size), n (number of draws), N (success states)

MixedFrequency

components (list of distributions), weights (mixing weights)

NegativeBinomial

r (number of successes), p (probability of success)

PanjerABk

a, b, k (Panjer parameters), tol (tolerance), max_iter (max iterations)

Poisson

mu (mean/rate parameter)

TriangularFrequency

c (mode), loc (minimum), scale (maximum - minimum)

Severity Distributions

Severity Distribution Parameters

Distribution

Parameters

Beta

a, b (shape parameters), loc, scale

ChiSquared

df (degrees of freedom), loc, scale

ConstantSeverity

value (fixed severity value)

ContinuousUniformSeverity

loc (minimum), scale (maximum - minimum)

DiscretizedSeverity

sev_dist (underlying distribution), min_val, max_val, bins

EmpiricalSeverity

values (data values), probs (probabilities)

Exponential

scale (rate = 1/scale), loc

Gamma

shape (alpha), loc, scale

InverseGamma

shape (alpha), loc, scale

InverseGaussian

shape (lambda), loc, scale (mu)

InverseWeibull

shape (c), loc, scale

Lognormal

shape (sigma), loc, scale

MixedSeverity

components (list of distributions), weights (mixing weights)

Pareto

b (shape/alpha), loc, scale

StudentsT

df (degrees of freedom), loc, scale

TriangularSeverity

c (mode), loc (minimum), scale (maximum - minimum)

Weibull

shape (c), loc, scale

Compound Distributions

All compound distributions use the same parameter structure:

  • frequency: A frequency distribution instance

  • severity: A severity distribution instance

Mixed Poisson Distributions

Mixed Poisson Distribution Parameters

Distribution

Parameters

PoissonGammaMixture

alpha, beta (Gamma mixing parameters)

PoissonInverseGaussianMixture

mu (mean), lambda_shape (shape parameter)

HierarchicalPoissonMixture

portfolio_alpha, portfolio_beta, group_alpha, n_groups

TimeVaryingPoissonMixture

base_rate, intensity_func, param_dist, time_horizon

Zero-Inflated Distributions

All zero-inflated distributions use:

  • frequency: Base frequency distribution

  • severity: Base severity distribution

  • zero_prob: Probability of zero claims

Migration Guide

If you’re updating from an older version, here are the key parameter changes:

# Old (pre-0.2.0)
lognormal = Lognormal(shape=1.5, location=0.0, scale=1.0)  # WRONG
pareto = Pareto(b=2.0, threshold=1000.0, scale=1.0)        # WRONG

# New (0.2.0+)
lognormal = Lognormal(shape=1.5, loc=0.0, scale=1.0)       # CORRECT
pareto = Pareto(b=2.0, loc=1000.0, scale=1.0)             # CORRECT

Best Practices

  1. Always use keyword arguments when creating distributions to avoid confusion:

    # Good
dist = Gamma(shape=2.0, loc=0.0, scale=1.0)

# Avoid
dist = Gamma(2.0, 0.0, 1.0)

  2. Check parameter bounds - some distributions have restrictions:

    # Pareto requires loc > 0 (minimum value)
pareto = Pareto(b=2.0, loc=1000.0, scale=1.0)  # loc must be positive

# Beta requires 0 <= x <= 1 after transformation
beta = Beta(a=2.0, b=3.0, loc=0.0, scale=1.0)

  3. Use consistent units across frequency and severity when creating compounds:

    freq = Poisson(mu=10)  # 10 claims per period
sev = Lognormal(shape=1.0, loc=0.0, scale=1000)  # severity in dollars
compound = CompoundPoisson(frequency=freq, severity=sev)

Examples

Creating Common Distributions

from quactuary.distributions import (
    Poisson, NegativeBinomial,
    Lognormal, Pareto, Gamma,
    CompoundPoisson
)

# Frequency distributions
poisson_freq = Poisson(mu=5.0)
negbin_freq = NegativeBinomial(r=10, p=0.3)

# Severity distributions
lognormal_sev = Lognormal(shape=1.5, loc=0.0, scale=1000.0)
pareto_sev = Pareto(b=2.0, loc=1000.0, scale=1.0)
gamma_sev = Gamma(shape=2.0, loc=0.0, scale=500.0)

# Compound distribution
compound = CompoundPoisson(
    frequency=poisson_freq,
    severity=lognormal_sev
)

Working with Zero-Inflated Models

from quactuary.distributions import ZeroInflatedCompound

# 20% chance of zero claims
zi_compound = ZeroInflatedCompound(
    frequency=Poisson(mu=5.0),
    severity=Gamma(shape=2.0, scale=1000.0),
    zero_prob=0.2
)

See Also