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"""
Exponential power density parameter calculator.
"""
__all__ = ["exppow_pars"]
from math import sqrt
from scipy.special import gamma
def exppow_pars(B):
r"""
Return w(B) and c(B) for the exponential power density:
.. math::
p(v|S,B) = \frac{w(B)}{S} \exp\left(-c(B) |v/S|^{2/(1+B)}\right)
*B* in (-1,1] is a measure of kurtosis::
B = 1: double exponential
B = 0: normal
B -> -1: uniform
[1] Thiemann, M., M. Trosser, H. Gupta, and S. Sorooshian (2001).
*Bayesian recursive parameter estimation for hydrologic models*,
Water Resour. Res. 37(10) 2521-2535.
"""
# First calculate some dummy variables
A1 = gamma(3 * (1 + B) / 2)
A2 = gamma((1 + B) / 2)
# And use these to derive Cb and Wb
cB = (A1 / A2) ** (1 / (1 + B))
wB = sqrt(A1 / A2**3) / (1 + B)
return cB, wB
def test():
import math
cB, wB = exppow_pars(13)
assert abs(cB - 12.8587702619708) < 1e-13
assert abs(wB - 5766.80847609837) < 1e-11
# Check that beta=0 yields a normal distribution
cB, wB = exppow_pars(0)
assert abs(2 * math.pi * wB**2 - 1) < 1e-14
assert abs(cB - 0.5) < 1e-14
if __name__ == "__main__":
# print calc_CbWb(13)
test()
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