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rickecon committed Dec 15, 2023
1 parent 187ca28 commit 45a0f03
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62 changes: 36 additions & 26 deletions code/gmm/distributions.py
Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
'''
"""
------------------------------------------------------------------------
This module contains the functions for probability density functions of
continuous PDF's.
Expand All @@ -8,21 +8,21 @@
GG_pdf()
GB2_pdf()
------------------------------------------------------------------------
'''
"""
# Import packages
import numpy as np
import scipy.special as spc


'''
"""
------------------------------------------------------------------------
Functions
------------------------------------------------------------------------
'''
"""


def LN_pdf(xvals, mu, sigma):
'''
"""
--------------------------------------------------------------------
This function gives the PDF of the lognormal distribution for xvals
given mu and sigma
Expand All @@ -46,16 +46,19 @@ def LN_pdf(xvals, mu, sigma):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = np.float64(((1 / (np.sqrt(2 * np.pi) * sigma * xvals)) *
np.exp((-1.0 / 2.0) *
(((np.log(xvals) - mu) / sigma) ** 2))))
"""
pdf_vals = np.float64(
(
(1 / (np.sqrt(2 * np.pi) * sigma * xvals))
* np.exp((-1.0 / 2.0) * (((np.log(xvals) - mu) / sigma) ** 2))
)
)

return pdf_vals


def GA_pdf(xvals, alpha, beta):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the two-parameter gamma (GA)
distribution. See McDonald and Xu (1995).
Expand All @@ -80,16 +83,18 @@ def GA_pdf(xvals, alpha, beta):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((1 / ((beta ** alpha) * spc.gamma(alpha))) *
(xvals ** (alpha - 1)) * np.exp(-xvals / beta))
"""
pdf_vals = np.float64(
(1 / ((beta**alpha) * spc.gamma(alpha)))
* (xvals ** (alpha - 1))
* np.exp(-xvals / beta)
)

return pdf_vals


def GG_pdf(xvals, alpha, beta, mm):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the three-parameter generalized gamma
(GG) distribution. See McDonald and Xu (1995).
Expand Down Expand Up @@ -118,17 +123,18 @@ def GG_pdf(xvals, alpha, beta, mm):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((mm / ((beta ** alpha) * spc.gamma(alpha / mm))) *
(xvals ** (alpha - 1)) *
np.exp(-((xvals / beta) ** mm)))
"""
pdf_vals = np.float64(
(mm / ((beta**alpha) * spc.gamma(alpha / mm)))
* (xvals ** (alpha - 1))
* np.exp(-((xvals / beta) ** mm))
)

return pdf_vals


def GB2_pdf(xvals, aa, bb, pp, qq):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the four-parameter generalized beta 2
(GB2) distribution. See McDonald and Xu (1995).
Expand Down Expand Up @@ -158,10 +164,14 @@ def GB2_pdf(xvals, aa, bb, pp, qq):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((aa * (xvals ** (aa * pp - 1))) / ((bb ** (aa * pp)) *
spc.beta(pp, qq) *
((1 + ((xvals / bb) ** aa)) ** (pp + qq))))
"""
pdf_vals = np.float64(
(aa * (xvals ** (aa * pp - 1)))
/ (
(bb ** (aa * pp))
* spc.beta(pp, qq)
* ((1 + ((xvals / bb) ** aa)) ** (pp + qq))
)
)

return pdf_vals
62 changes: 36 additions & 26 deletions code/mle/distributions.py
Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
'''
"""
------------------------------------------------------------------------
This module contains the functions for probability density functions of
continuous PDF's.
Expand All @@ -8,21 +8,21 @@
GG_pdf()
GB2_pdf()
------------------------------------------------------------------------
'''
"""
# Import packages
import numpy as np
import scipy.special as spc


'''
"""
------------------------------------------------------------------------
Functions
------------------------------------------------------------------------
'''
"""


def LN_pdf(xvals, mu, sigma):
'''
"""
--------------------------------------------------------------------
This function gives the PDF of the lognormal distribution for xvals
given mu and sigma
Expand All @@ -46,16 +46,19 @@ def LN_pdf(xvals, mu, sigma):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = np.float64(((1 / (np.sqrt(2 * np.pi) * sigma * xvals)) *
np.exp((-1.0 / 2.0) *
(((np.log(xvals) - mu) / sigma) ** 2))))
"""
pdf_vals = np.float64(
(
(1 / (np.sqrt(2 * np.pi) * sigma * xvals))
* np.exp((-1.0 / 2.0) * (((np.log(xvals) - mu) / sigma) ** 2))
)
)

return pdf_vals


def GA_pdf(xvals, alpha, beta):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the two-parameter gamma (GA)
distribution. See McDonald and Xu (1995).
Expand All @@ -80,16 +83,18 @@ def GA_pdf(xvals, alpha, beta):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((1 / ((beta ** alpha) * spc.gamma(alpha))) *
(xvals ** (alpha - 1)) * np.exp(-xvals / beta))
"""
pdf_vals = np.float64(
(1 / ((beta**alpha) * spc.gamma(alpha)))
* (xvals ** (alpha - 1))
* np.exp(-xvals / beta)
)

return pdf_vals


def GG_pdf(xvals, alpha, beta, mm):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the three-parameter generalized gamma
(GG) distribution. See McDonald and Xu (1995).
Expand Down Expand Up @@ -118,17 +123,18 @@ def GG_pdf(xvals, alpha, beta, mm):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((mm / ((beta ** alpha) * spc.gamma(alpha / mm))) *
(xvals ** (alpha - 1)) *
np.exp(-((xvals / beta) ** mm)))
"""
pdf_vals = np.float64(
(mm / ((beta**alpha) * spc.gamma(alpha / mm)))
* (xvals ** (alpha - 1))
* np.exp(-((xvals / beta) ** mm))
)

return pdf_vals


def GB2_pdf(xvals, aa, bb, pp, qq):
'''
"""
--------------------------------------------------------------------
Returns the PDF values from the four-parameter generalized beta 2
(GB2) distribution. See McDonald and Xu (1995).
Expand Down Expand Up @@ -158,10 +164,14 @@ def GB2_pdf(xvals, aa, bb, pp, qq):
RETURNS: pdf_vals
--------------------------------------------------------------------
'''
pdf_vals = \
np.float64((aa * (xvals ** (aa * pp - 1))) / ((bb ** (aa * pp)) *
spc.beta(pp, qq) *
((1 + ((xvals / bb) ** aa)) ** (pp + qq))))
"""
pdf_vals = np.float64(
(aa * (xvals ** (aa * pp - 1)))
/ (
(bb ** (aa * pp))
* spc.beta(pp, qq)
* ((1 + ((xvals / bb) ** aa)) ** (pp + qq))
)
)

return pdf_vals

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