neutonsevero
9aa97fc3d4
`generate_data.py` for processing and fitting statistical distributions to data. 'distributions.py' to create new dists to fit 'analysis_data.ipynb" notebook for data analysis
44 lines
1.3 KiB
Python
44 lines
1.3 KiB
Python
from scipy.stats import rv_continuous
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from scipy.special import gamma, 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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import pandas as pd
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class k_gen(rv_continuous):
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"""K distribution for radar clutter modeling.
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The probability density function is::
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f(x; nu, b) = 2/Gamma(nu) * b^((nu+1)/2) * x^((nu-1)/2) * K_{nu-1}(2*sqrt(b*x))
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for x >= 0, where K_{nu-1} is the modified Bessel function of the second
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kind of order nu-1, nu > 0 is the shape parameter and b > 0 is the rate
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parameter.
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"""
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def _shape_info(self):
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return [_ShapeInfo("nu", domain=(0, np.inf), inclusive=(False, True)),
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_ShapeInfo("b", domain=(0, np.inf), inclusive=(False, True))]
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def _argcheck(self, nu, b):
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return (nu > 0) & (b > 0)
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def _pdf(self, x, nu, b):
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# k.pdf(x, nu, b) = 2/Gamma(nu) * b^((nu+1)/2) * x^((nu-1)/2) * K_{nu-1}(2*sqrt(b*x))
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return np.exp(self._logpdf(x, nu, b))
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def _logpdf(self, x, nu, b):
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return (
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np.log(2.0)
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- gammaln(nu)
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+ (nu + 1) / 2.0 * np.log(b)
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+ (nu - 1) / 2.0 * np.log(x)
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+ np.log(kv(nu - 1, 2.0 * np.sqrt(b * x)))
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)
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k_dist = k_gen(a=0.0, name="k_distribution", shapes="nu, b")
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