Source code for bumps.dream.exppow

"""
Exponential power density parameter calculator.
"""

from __future__ import division

__all__ = ["exppow_pars"]

from math import sqrt

from scipy.special import gamma

[docs]
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()