neutonsevero
d07590e73d
ruff for code formatting BIC statistic AND BIC test implemented test_distributions.py for test new created dists with pytest REFACTOR: k_gen pdf changed from 2 params to generalized
52 lines
1.7 KiB
Python
52 lines
1.7 KiB
Python
from scipy.stats import rv_continuous
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from scipy.special import kv, gammaln
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from scipy.stats._distn_infrastructure import _ShapeInfo
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import numpy as np
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class k_gen(rv_continuous):
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"""Generalized K distribution for radar clutter modeling.
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The probability density function is::
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f(x; mu, alpha, beta) = 2 / (Gamma(alpha) * Gamma(beta))
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* (alpha*beta/mu)^((alpha+beta)/2)
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* x^((alpha+beta)/2 - 1)
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* K_{alpha-beta}(2*sqrt(alpha*beta*x/mu))
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for x > 0, where K_{alpha-beta} is the modified Bessel function of the
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second kind of order alpha-beta, mu > 0 is the mean, and alpha > 0,
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beta > 0 are shape parameters.
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The standard (2-parameter) K distribution is the special case beta=1,
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with nu=alpha and b=alpha/mu.
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"""
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def _shape_info(self):
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return [
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_ShapeInfo("mu", domain=(0, np.inf), inclusive=(False, True)),
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_ShapeInfo("alpha", domain=(0, np.inf), inclusive=(True, True)),
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_ShapeInfo("beta", domain=(0, np.inf), inclusive=(True, True)),
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]
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def _argcheck(self, mu, alpha, beta):
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return (mu > 0) & (alpha > 0) & (beta > 0)
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def _pdf(self, x, mu, alpha, beta):
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return np.exp(self._logpdf(x, mu, alpha, beta))
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def _logpdf(self, x, mu, alpha, beta):
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z = 2.0 * np.sqrt(alpha * beta * x / mu)
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return (
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np.log(2.0)
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- gammaln(alpha)
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- gammaln(beta)
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+ (alpha + beta) / 2.0 * np.log(alpha * beta / mu)
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+ ((alpha + beta) / 2.0 - 1.0) * np.log(x)
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+ np.log(kv(alpha - beta, z))
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)
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k_dist = k_gen(a=0.0, name="k_distribution", shapes="mu, alpha, beta")
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