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‎code/gmm/distributions.py‎

Lines changed: 36 additions & 26 deletions
Original file line numberDiff line numberDiff line change
@@ -1,4 +1,4 @@
1-
'''
1+
"""
22
------------------------------------------------------------------------
33
This module contains the functions for probability density functions of
44
continuous PDF's.
@@ -8,21 +8,21 @@
88
GG_pdf()
99
GB2_pdf()
1010
------------------------------------------------------------------------
11-
'''
11+
"""
1212
# Import packages
1313
import numpy as np
1414
import scipy.special as spc
1515

1616

17-
'''
17+
"""
1818
------------------------------------------------------------------------
1919
Functions
2020
------------------------------------------------------------------------
21-
'''
21+
"""
2222

2323

2424
def LN_pdf(xvals, mu, sigma):
25-
'''
25+
"""
2626
--------------------------------------------------------------------
2727
This function gives the PDF of the lognormal distribution for xvals
2828
given mu and sigma
@@ -46,16 +46,19 @@ def LN_pdf(xvals, mu, sigma):
4646
4747
RETURNS: pdf_vals
4848
--------------------------------------------------------------------
49-
'''
50-
pdf_vals = np.float64(((1 / (np.sqrt(2 * np.pi) * sigma * xvals)) *
51-
np.exp((-1.0 / 2.0) *
52-
(((np.log(xvals) - mu) / sigma) ** 2))))
49+
"""
50+
pdf_vals = np.float64(
51+
(
52+
(1 / (np.sqrt(2 * np.pi) * sigma * xvals))
53+
* np.exp((-1.0 / 2.0) * (((np.log(xvals) - mu) / sigma) ** 2))
54+
)
55+
)
5356

5457
return pdf_vals
5558

5659

5760
def GA_pdf(xvals, alpha, beta):
58-
'''
61+
"""
5962
--------------------------------------------------------------------
6063
Returns the PDF values from the two-parameter gamma (GA)
6164
distribution. See McDonald and Xu (1995).
@@ -80,16 +83,18 @@ def GA_pdf(xvals, alpha, beta):
8083
8184
RETURNS: pdf_vals
8285
--------------------------------------------------------------------
83-
'''
84-
pdf_vals = \
85-
np.float64((1 / ((beta ** alpha) * spc.gamma(alpha))) *
86-
(xvals ** (alpha - 1)) * np.exp(-xvals / beta))
86+
"""
87+
pdf_vals = np.float64(
88+
(1 / ((beta**alpha) * spc.gamma(alpha)))
89+
* (xvals ** (alpha - 1))
90+
* np.exp(-xvals / beta)
91+
)
8792

8893
return pdf_vals
8994

9095

9196
def GG_pdf(xvals, alpha, beta, mm):
92-
'''
97+
"""
9398
--------------------------------------------------------------------
9499
Returns the PDF values from the three-parameter generalized gamma
95100
(GG) distribution. See McDonald and Xu (1995).
@@ -118,17 +123,18 @@ def GG_pdf(xvals, alpha, beta, mm):
118123
119124
RETURNS: pdf_vals
120125
--------------------------------------------------------------------
121-
'''
122-
pdf_vals = \
123-
np.float64((mm / ((beta ** alpha) * spc.gamma(alpha / mm))) *
124-
(xvals ** (alpha - 1)) *
125-
np.exp(-((xvals / beta) ** mm)))
126+
"""
127+
pdf_vals = np.float64(
128+
(mm / ((beta**alpha) * spc.gamma(alpha / mm)))
129+
* (xvals ** (alpha - 1))
130+
* np.exp(-((xvals / beta) ** mm))
131+
)
126132

127133
return pdf_vals
128134

129135

130136
def GB2_pdf(xvals, aa, bb, pp, qq):
131-
'''
137+
"""
132138
--------------------------------------------------------------------
133139
Returns the PDF values from the four-parameter generalized beta 2
134140
(GB2) distribution. See McDonald and Xu (1995).
@@ -158,10 +164,14 @@ def GB2_pdf(xvals, aa, bb, pp, qq):
158164
159165
RETURNS: pdf_vals
160166
--------------------------------------------------------------------
161-
'''
162-
pdf_vals = \
163-
np.float64((aa * (xvals ** (aa * pp - 1))) / ((bb ** (aa * pp)) *
164-
spc.beta(pp, qq) *
165-
((1 + ((xvals / bb) ** aa)) ** (pp + qq))))
167+
"""
168+
pdf_vals = np.float64(
169+
(aa * (xvals ** (aa * pp - 1)))
170+
/ (
171+
(bb ** (aa * pp))
172+
* spc.beta(pp, qq)
173+
* ((1 + ((xvals / bb) ** aa)) ** (pp + qq))
174+
)
175+
)
166176

167177
return pdf_vals

‎code/mle/distributions.py‎

Lines changed: 36 additions & 26 deletions
Original file line numberDiff line numberDiff line change
@@ -1,4 +1,4 @@
1-
'''
1+
"""
22
------------------------------------------------------------------------
33
This module contains the functions for probability density functions of
44
continuous PDF's.
@@ -8,21 +8,21 @@
88
GG_pdf()
99
GB2_pdf()
1010
------------------------------------------------------------------------
11-
'''
11+
"""
1212
# Import packages
1313
import numpy as np
1414
import scipy.special as spc
1515

1616

17-
'''
17+
"""
1818
------------------------------------------------------------------------
1919
Functions
2020
------------------------------------------------------------------------
21-
'''
21+
"""
2222

2323

2424
def LN_pdf(xvals, mu, sigma):
25-
'''
25+
"""
2626
--------------------------------------------------------------------
2727
This function gives the PDF of the lognormal distribution for xvals
2828
given mu and sigma
@@ -46,16 +46,19 @@ def LN_pdf(xvals, mu, sigma):
4646
4747
RETURNS: pdf_vals
4848
--------------------------------------------------------------------
49-
'''
50-
pdf_vals = np.float64(((1 / (np.sqrt(2 * np.pi) * sigma * xvals)) *
51-
np.exp((-1.0 / 2.0) *
52-
(((np.log(xvals) - mu) / sigma) ** 2))))
49+
"""
50+
pdf_vals = np.float64(
51+
(
52+
(1 / (np.sqrt(2 * np.pi) * sigma * xvals))
53+
* np.exp((-1.0 / 2.0) * (((np.log(xvals) - mu) / sigma) ** 2))
54+
)
55+
)
5356

5457
return pdf_vals
5558

5659

5760
def GA_pdf(xvals, alpha, beta):
58-
'''
61+
"""
5962
--------------------------------------------------------------------
6063
Returns the PDF values from the two-parameter gamma (GA)
6164
distribution. See McDonald and Xu (1995).
@@ -80,16 +83,18 @@ def GA_pdf(xvals, alpha, beta):
8083
8184
RETURNS: pdf_vals
8285
--------------------------------------------------------------------
83-
'''
84-
pdf_vals = \
85-
np.float64((1 / ((beta ** alpha) * spc.gamma(alpha))) *
86-
(xvals ** (alpha - 1)) * np.exp(-xvals / beta))
86+
"""
87+
pdf_vals = np.float64(
88+
(1 / ((beta**alpha) * spc.gamma(alpha)))
89+
* (xvals ** (alpha - 1))
90+
* np.exp(-xvals / beta)
91+
)
8792

8893
return pdf_vals
8994

9095

9196
def GG_pdf(xvals, alpha, beta, mm):
92-
'''
97+
"""
9398
--------------------------------------------------------------------
9499
Returns the PDF values from the three-parameter generalized gamma
95100
(GG) distribution. See McDonald and Xu (1995).
@@ -118,17 +123,18 @@ def GG_pdf(xvals, alpha, beta, mm):
118123
119124
RETURNS: pdf_vals
120125
--------------------------------------------------------------------
121-
'''
122-
pdf_vals = \
123-
np.float64((mm / ((beta ** alpha) * spc.gamma(alpha / mm))) *
124-
(xvals ** (alpha - 1)) *
125-
np.exp(-((xvals / beta) ** mm)))
126+
"""
127+
pdf_vals = np.float64(
128+
(mm / ((beta**alpha) * spc.gamma(alpha / mm)))
129+
* (xvals ** (alpha - 1))
130+
* np.exp(-((xvals / beta) ** mm))
131+
)
126132

127133
return pdf_vals
128134

129135

130136
def GB2_pdf(xvals, aa, bb, pp, qq):
131-
'''
137+
"""
132138
--------------------------------------------------------------------
133139
Returns the PDF values from the four-parameter generalized beta 2
134140
(GB2) distribution. See McDonald and Xu (1995).
@@ -158,10 +164,14 @@ def GB2_pdf(xvals, aa, bb, pp, qq):
158164
159165
RETURNS: pdf_vals
160166
--------------------------------------------------------------------
161-
'''
162-
pdf_vals = \
163-
np.float64((aa * (xvals ** (aa * pp - 1))) / ((bb ** (aa * pp)) *
164-
spc.beta(pp, qq) *
165-
((1 + ((xvals / bb) ** aa)) ** (pp + qq))))
167+
"""
168+
pdf_vals = np.float64(
169+
(aa * (xvals ** (aa * pp - 1)))
170+
/ (
171+
(bb ** (aa * pp))
172+
* spc.beta(pp, qq)
173+
* ((1 + ((xvals / bb) ** aa)) ** (pp + qq))
174+
)
175+
)
166176

167177
return pdf_vals

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