/
pln_distrib.py
48 lines (33 loc) · 1.29 KB
/
pln_distrib.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
'''
Implementation in scipy form of the Double Pareto-Lognormal Distribution
'''
import numpy as np
from scipy.stats import rv_continuous, norm
def _pln_pdf(x, alpha, nu, tau2):
A1 = np.exp(alpha * nu + alpha ** 2 * tau2 / 2)
fofx = alpha * A1 * x ** (-alpha - 1) *\
norm.cdf((np.log(x) - nu - alpha * tau2) / np.sqrt(tau2))
return fofx
def _pln_cdf(x, alpha, nu, tau2):
A1 = np.exp(alpha * nu + alpha ** 2 * tau2 / 2)
term1 = norm.cdf((np.log(x) - nu) / np.sqrt(tau2))
term2 = x ** (-alpha) * A1 * \
norm.cdf((np.log(x) - nu - alpha * tau2) / np.sqrt(tau2))
return term1 - term2
def _pln_logpdf(x, alpha, nu, tau2):
return np.log(alpha) + alpha * nu + alpha * tau2 / 2 - \
(alpha + 1) * np.log(x) + \
norm.logcdf((np.log(x) - nu - alpha * tau2) / np.sqrt(tau2))
def _pln_rawmoments(r, alpha, nu, tau2):
if alpha > r:
return alpha / (alpha - r) * np.exp(r*nu + r**2.*tau2/2)
else:
return np.NaN
class pln_gen(rv_continuous):
def _pdf(self, x, alpha, nu, tau2):
return _pln_pdf(x, alpha, nu, tau2)
def _logpdf(self, x, alpha, nu, tau2):
return _pln_logpdf(x, alpha, nu, tau2)
def _cdf(self, x, alpha, nu, tau2):
return _pln_cdf(x, alpha, nu, tau2)
pln = pln_gen(name="pln", a=0.0)