441 lines
16 KiB
Python
441 lines
16 KiB
Python
from dataclasses import dataclass, field
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import numpy as np
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import plotly.graph_objects as go
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import matplotlib.pyplot as plt
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import seaborn as sns
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from scipy.stats import rv_continuous, goodness_of_fit
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from plotly.subplots import make_subplots
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@dataclass
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class DistributionSummary:
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"""
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Summary of a single distribution fit against a dataset.
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Attributes
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----------
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distribution_object : rv_continuous
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The scipy distribution object used for fitting.
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distribution_name : str
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Human-readable name of the distribution.
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args_fit_params : tuple
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Initial guess positional parameters passed to fit() (empty tuple if none).
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kwds_fit_params : dict
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Keyword arguments that were passed to fit() (fixed params, etc.).
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fit_result_params : tuple
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The actual fitted parameters returned by fit() (empty tuple until fit() is called).
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statistic_method : object
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GoF statistic identifier used in validate() (e.g. 'ad', 'ks' or a custom callable).
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test_result : object
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Result object from scipy.stats.goodness_of_fit; None until
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validate() is called. Exposes .statistic and .pvalue.
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Computed properties
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-------------------
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pvalue : float | None – p-value from the GoF test
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gof_statistic : float | None – test statistic from the GoF test
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mean : float – mean of the fitted distribution
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std : float – standard deviation of the fitted distribution
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var : float – variance of the fitted distribution
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"""
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distribution_object: rv_continuous
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distribution_name: str
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args_fit_params: tuple = field(default_factory=tuple)
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kwds_fit_params: dict = field(default_factory=dict)
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fit_result_params: tuple = field(default_factory=tuple)
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statistic_method: object = "ad"
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test_result: object = None
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# ── convenience properties ────────────────────────────────────────────────
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@property
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def pvalue(self) -> float | None:
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"""p-value from the goodness-of-fit test, or None if not yet run."""
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return self.test_result.pvalue if self.test_result is not None else None
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@property
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def gof_statistic(self) -> float | None:
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"""Test statistic from the goodness-of-fit test, or None if not yet run."""
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return self.test_result.statistic if self.test_result is not None else None
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@property
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def mean(self) -> float:
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"""Mean of the fitted distribution."""
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return float(self.distribution_object.mean(*self.fit_result_params))
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@property
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def std(self) -> float:
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"""Standard deviation of the fitted distribution."""
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return float(self.distribution_object.std(*self.fit_result_params))
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@property
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def var(self) -> float:
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"""Variance of the fitted distribution."""
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return float(self.distribution_object.var(*self.fit_result_params))
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def __repr__(self) -> str:
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pval_str = f"{self.pvalue:.4f}" if self.pvalue is not None else "N/A"
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stat_str = (
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f"{self.gof_statistic:.4f}" if self.gof_statistic is not None else "N/A"
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)
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return (
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f"DistributionSummary({self.distribution_name})"
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f" params={self.fit_result_params}"
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f" mean={self.mean:.4f} std={self.std:.4f}"
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f" GoF[{self.statistic_method}]={stat_str} p={pval_str}"
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)
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def __str__(self) -> str:
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return self.__repr__()
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class Fitter:
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"""
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Fits and evaluates multiple distributions against a dataset.
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Parameters
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----------
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dist_list : list[rv_continuous]
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Distributions to fit.
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statistic_method : str
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Goodness-of-fit statistic passed to goodness_of_fit (default 'ad').
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**kwargs :
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Per-distribution initial guesses and fixed parameters, keyed as:
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- ``<dist.name>_args`` : tuple of positional initial guesses
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- ``<dist.name>_params`` : dict of keyword fixed parameters
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Example:
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Fitter(
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[gamma, weibull_min],
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gamma_args=(2.0,),
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gamma_params={'floc': 0},
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weibull_min_args=(1.5, 0.0, 1.0),
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)
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"""
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def __init__(
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self, dist_list: list[rv_continuous], statistic_method: str = "ad", **kwargs
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):
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self._dist: dict[str, DistributionSummary] = {}
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self.dist_list = list(dist_list) # Ensure it's a list for multiple iterations
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for dist in dist_list:
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self._dist[dist.name] = DistributionSummary(
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distribution_object=dist,
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distribution_name=dist.name,
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args_fit_params=kwargs.get(f"{dist.name}_args", ()),
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kwds_fit_params=kwargs.get(f"{dist.name}_params", {}),
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statistic_method=statistic_method,
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test_result=None,
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)
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def _resolve_key(self, key: str | rv_continuous) -> str:
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"""Resolve a distribution name or rv_continuous object to its string key."""
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name = key.name if isinstance(key, rv_continuous) else key
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if name not in self._dist:
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available = ", ".join(self._dist)
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raise KeyError(f"Distribution '{name}' not found. Available: {available}")
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return name
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def __contains__(self, key: str | rv_continuous) -> bool:
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name = key.name if isinstance(key, rv_continuous) else key
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return name in self._dist
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def __getitem__(self, key: str | rv_continuous) -> DistributionSummary:
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return self._dist[self._resolve_key(key)]
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def __setitem__(
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self, key: str | rv_continuous, summary: DistributionSummary
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) -> None:
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if not isinstance(summary, DistributionSummary):
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raise TypeError(
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f"Expected DistributionSummary, got {type(summary).__name__}."
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)
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self._dist[self._resolve_key(key)] = summary
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def __iter__(self):
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return self
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def __next__(self):
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if not hasattr(self, "_iter_index"):
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self._iter_index = 0
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if self._iter_index >= len(self._dist):
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del self._iter_index
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raise StopIteration
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key = list(self._dist.keys())[self._iter_index]
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summary = self._dist[key]
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self._iter_index += 1
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return key, summary
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def fit(self, data: np.ndarray) -> dict[str, DistributionSummary]:
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"""
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Fit every distribution to *data* via MLE.
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Parameters
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----------
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data : array-like
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Input data. Only the absolute value is used.
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Returns
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-------
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dict[str, DistributionSummary]
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Mapping of distribution name → summary (test_result is None
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until validate() is called).
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"""
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data_flat = np.abs(data).flatten()
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self._last_data_flat = data_flat
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for dist in self.dist_list:
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_summary = self._dist[dist.name]
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fit_params = dist.fit(
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data_flat, *_summary.args_fit_params, **_summary.kwds_fit_params
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)
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_summary.fit_result_params = fit_params
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self._dist[dist.name] = _summary
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def validate(self, **kwargs) -> dict[str, DistributionSummary]:
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"""
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Run the goodness-of-fit test on every previously fitted distribution.
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Parameters
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----------
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**kwargs :
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Extra keyword arguments forwarded to goodness_of_fit()
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(e.g. n_mc_samples=100).
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Returns
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-------
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dict[str, DistributionSummary]
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Same results dict, with test_result populated for each distribution.
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"""
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if not hasattr(self, "_last_data_flat"):
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raise RuntimeError("No data available. Call fit() first.")
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data_flat = self._last_data_flat
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for dist in self.dist_list:
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_summary = self._dist[dist.name]
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test_result = goodness_of_fit(
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dist, data_flat, statistic=_summary.statistic_method, **kwargs
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)
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_summary.test_result = test_result
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self._dist[dist.name] = _summary
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def summary(self) -> dict[str, DistributionSummary]:
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"""
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Print a summary of all fitted distributions, including parameters and GoF results.
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"""
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for dist_name, summary in self._dist.items():
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print(summary)
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def plot_qq_plots(self, method: str = "hazen"):
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"""
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Generate QQ plots for each fitted distribution against the data.
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Requires that fit() and validate() have been called to populate parameters and test results.
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Parameters
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----------
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method : str
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Plotting positions formula. Either 'hazen' (default) or 'filliben'.
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- 'hazen' : p_i = (i - 0.5) / n
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- 'filliben': p_1 = 1 - 0.5^(1/n), p_n = 0.5^(1/n),
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p_i = (i - 0.3175) / (n + 0.365) for 1 < i < n
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"""
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if not hasattr(self, "_last_data_flat"):
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raise RuntimeError("No data available. Call fit() first.")
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if method not in ("hazen", "filliben"):
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raise ValueError(f"method must be 'hazen' or 'filliben', got '{method}'.")
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data_flat = self._last_data_flat
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# generate subplots with 2 columns and as many rows as needed, but not more than 3 rows, if there are more than 6 distributions, create multiple figures
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num_dists = len(self._dist)
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num_cols = 2
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num_rows = min(3, (num_dists + 1) // 2)
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fig = make_subplots(
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rows=num_rows,
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cols=num_cols,
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subplot_titles=[dist_name for dist_name in self._dist.keys()],
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)
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for dist_name, summary in self:
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if summary.test_result is None:
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print(
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f"Distribution '{dist_name}' has not been validated yet. Skipping QQ plot."
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)
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continue
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# Generate theoretical quantiles
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sorted_data = np.sort(data_flat)
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n = len(sorted_data)
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i = np.arange(1, n + 1)
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if method == "hazen":
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plotting_positions = (i - 0.5) / n
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else: # filliben
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plotting_positions = (i - 0.3175) / (n + 0.365)
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plotting_positions[0] = 1 - 0.5 ** (1 / n)
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plotting_positions[-1] = 0.5 ** (1 / n)
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theoretical_quantiles = summary.distribution_object.ppf(
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plotting_positions, *summary.fit_result_params
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)
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# Create QQ plot in each subplot
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row = (list(self._dist.keys()).index(dist_name) // num_cols) + 1
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col = (list(self._dist.keys()).index(dist_name) % num_cols) + 1
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fig.add_trace(
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go.Scatter(
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x=theoretical_quantiles,
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y=sorted_data,
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mode="markers",
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name=dist_name,
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),
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row=row,
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col=col,
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)
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# Add a reference line y=x
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min_val = min(theoretical_quantiles.min(), sorted_data.min())
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max_val = max(theoretical_quantiles.max(), sorted_data.max())
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fig.add_trace(
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go.Scatter(
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x=[min_val, max_val],
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y=[min_val, max_val],
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mode="lines",
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name="y=x",
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line=dict(dash="dash"),
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),
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row=row,
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col=col,
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)
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fig.update_xaxes(title_text="Theoretical Quantiles", row=row, col=col)
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fig.update_yaxes(title_text="Empirical Quantiles", row=row, col=col)
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# add statistic value in bottom right of each subplot (summary.gof_statistic())
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fig.add_annotation(
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x=0.95,
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y=0.05,
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xref="x domain",
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yref="y domain",
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text=f"{summary.statistic_method}={summary.gof_statistic:.4f}",
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showarrow=False,
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font=dict(size=10, color="green" if summary.pvalue > 0.05 else "red"),
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row=row,
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col=col,
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)
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fig.update_layout(
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title=f"QQ Plots of Fitted Distributions ({method})",
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showlegend=False,
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autosize=True,
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)
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return fig
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def histogram_with_fits(self):
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"""
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Generate a histogram of the data with overlaid PDFs of each fitted distribution.
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Requires that fit() has been called to populate parameters.
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"""
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if not hasattr(self, "_last_data_flat"):
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raise RuntimeError("No data available. Call fit() first.")
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data_flat = self._last_data_flat
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x = np.linspace(0, data_flat.max(), 1000)
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fig = go.Figure(layout=go.Layout(hovermode="x unified"))
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# do not show data in hoover, only show the distribution name, p-value and GoF statistic for each distribution
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fig.add_trace(
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go.Histogram(
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x=data_flat,
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name="Data",
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opacity=0.3,
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histnorm="probability density",
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hoverinfo="skip",
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marker_color="blue",
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)
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)
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for dist_name, summary in self._dist.items():
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if not summary.fit_result_params:
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print(
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f"Distribution '{dist_name}' has not been fitted yet. Skipping PDF overlay."
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)
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continue
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pdf_values = summary.distribution_object.pdf(x, *summary.fit_result_params)
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# add trace and stack hoover x like stock price, but make the y value shows the p-value and GoF statistic for each distribution
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fig.add_trace(
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go.Scatter(
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x=x,
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y=pdf_values,
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mode="lines",
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name=f"{summary.distribution_name} Fit",
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)
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)
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hover_text = [
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f"<b>{summary.distribution_name}</b> p-value: {summary.pvalue:.4f} GoF: {summary.gof_statistic:.4f}"
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for _ in x
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]
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fig.data[-1].update(hovertext=hover_text, hoverinfo="text")
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# add grid
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fig.update_layout(xaxis=dict(showgrid=True), yaxis=dict(showgrid=True))
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# put title in top left, make it smaller, change it font to sans and put in light gray
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fig.update_layout(
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title=dict(
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text="Histogram of Data with Fitted Distributions",
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x=0.02,
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y=0.95,
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xanchor="left",
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yanchor="top",
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font=dict(size=20, color="darkgray", family="sans-serif"),
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),
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xaxis_title="Value",
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yaxis_title="Density",
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autosize=True,
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)
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return fig
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def histogram_with_fits_seaborn(self):
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"""
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Generate a histogram of the data with overlaid PDFs of each fitted distribution using seaborn.
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Requires that fit() has been called to populate parameters.
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"""
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if not hasattr(self, "_last_data_flat"):
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raise RuntimeError("No data available. Call fit() first.")
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data_flat = self._last_data_flat
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x = np.linspace(0, data_flat.max(), 1000)
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fig, ax = plt.subplots(figsize=(10, 6))
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sns.histplot(
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data_flat,
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bins=int(np.sqrt(len(data_flat))),
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kde=False,
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stat="density",
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color="blue",
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alpha=0.2,
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ax=ax,
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)
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for dist_name, summary in self._dist.items():
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if not summary.fit_result_params:
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print(
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f"Distribution '{dist_name}' has not been fitted yet. Skipping PDF overlay."
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)
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continue
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pdf_values = summary.distribution_object.pdf(x, *summary.fit_result_params)
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ax.plot(
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x,
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pdf_values,
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label=f"{summary.distribution_name} --- p={summary.pvalue:.4f}",
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)
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# put title in top left, make it smaller, change it font to sans and put in light gray
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ax.set_title(
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"Histogram of Data with Fitted Distributions",
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fontsize=8,
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loc="left",
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color="darkgray",
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fontfamily="sans-serif",
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)
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ax.set_xlabel("Value")
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ax.set_ylabel("Density")
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ax.legend()
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ax.grid(True)
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return fig
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