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r
e
t
h
e
tw
o
a
p
p
r
o
a
c
h
e
s
u
s
e
d
i
n
es
tim
a
t
i
o
n
th
e
o
r
y
t
o
e
s
t
im
a
te
p
o
p
u
l
a
t
i
o
n
p
a
r
am
e
t
e
r
s
g
iv
en
d
a
t
a
d
is
t
r
i
b
u
t
i
o
n
[
8
]
.
T
h
e
B
ay
es
i
an
a
p
p
r
o
a
c
h
is
an
es
tim
a
ti
o
n
m
e
th
o
d
t
h
a
t
c
o
m
b
in
es
a
p
r
i
o
r
d
i
s
t
r
i
b
u
t
i
o
n
an
d
a
s
am
p
l
e
d
i
s
t
r
i
b
u
t
i
o
n
[
9
]
.
T
h
e
B
ay
es
ia
n
a
p
p
r
o
a
ch
h
as
s
ev
er
a
l
m
e
th
o
d
s
,
o
n
e
o
f
w
h
ic
h
is
l
in
ea
r
ex
p
o
n
en
ti
a
l
l
o
s
s
f
u
n
c
t
i
o
n
.
Pa
r
am
e
t
e
r
e
s
t
im
a
tio
n
r
es
e
a
r
ch
u
s
in
g
th
e
lin
e
a
r
ex
p
o
n
e
n
t
i
al
m
e
th
o
d
in
t
h
e
B
ay
e
s
a
p
p
r
o
a
ch
i
s
c
o
n
s
i
d
e
r
e
d
g
o
o
d
a
n
d
m
o
s
t
c
o
m
m
o
n
ly
u
s
e
d
[
1
0
]
.
T
h
e
e
x
p
e
c
t
e
d
v
a
l
u
e
o
f
th
e
l
in
e
a
r
e
x
p
o
n
e
n
t
i
al
l
o
s
s
f
u
n
c
t
i
o
n
is
m
in
im
iz
e
d
w
h
en
u
s
i
n
g
t
h
e
l
in
e
a
r
e
x
p
o
n
e
n
t
i
al
m
e
th
o
d
f
o
r
p
a
r
am
et
e
r
e
s
t
im
a
ti
o
n
.
I
n
th
e
B
a
y
e
s
ia
n
m
e
th
o
d
,
th
e
p
ar
am
eter
i
s
tr
ea
ted
as
a
r
an
d
o
m
v
ar
iab
le
t
h
at
h
as
a
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
[
1
1
]
.
T
h
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
o
f
u
n
k
n
o
w
n
p
ar
am
eter
s
s
elec
ted
b
ased
o
n
t
w
o
ap
p
r
o
ac
h
es,
n
a
m
e
l
y
s
u
b
j
ec
tiv
e
an
d
b
ased
o
n
p
r
ev
io
u
s
r
esear
ch
i
s
ca
lled
th
e
p
r
io
r
d
is
tr
ib
u
tio
n
.
Pr
i
o
r
d
i
s
t
r
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b
u
t
i
o
n
s
c
o
n
s
i
s
t
o
f
tw
o
ty
p
es
,
n
am
e
ly
in
f
o
r
m
a
t
iv
e
p
r
i
o
r
d
i
s
t
r
i
b
u
t
i
o
n
s
an
d
n
o
n
-
in
f
o
r
m
a
t
iv
e
p
r
i
o
r
d
is
t
r
i
b
u
t
i
o
n
s
.
A
n
o
n
-
in
f
o
r
m
at
iv
e
p
r
i
o
r
d
i
s
t
r
i
b
u
ti
o
n
is
a
p
r
i
o
r
d
i
s
tr
i
b
u
ti
o
n
f
o
r
w
h
i
ch
n
o
in
f
o
r
m
ati
o
n
a
b
o
u
t
th
e
p
a
r
am
et
e
r
θ
is
k
n
o
w
n
,
o
n
e
o
f
w
h
i
ch
i
s
t
h
e
J
ef
f
r
ey
’
s
p
r
i
o
r
[
1
2
]
.
T
h
e
n
o
n
-
in
f
o
r
m
at
iv
e
p
r
i
o
r
d
i
s
t
r
i
b
u
t
io
n
h
as
a
l
es
s
s
ig
n
if
i
c
an
t in
f
lu
en
c
e
o
n
th
e
p
o
s
t
e
r
i
o
r
d
i
s
t
r
i
b
u
ti
o
n
,
b
u
t
w
i
ll
s
t
i
ll
h
av
e
a
n
in
f
lu
en
ce
o
n
t
h
e
an
a
ly
s
i
s
r
e
s
u
l
ts
.
T
h
e
an
a
ly
s
is
r
e
s
u
l
t
s
f
r
o
m
n
o
n
-
in
f
o
r
m
at
iv
e
p
r
i
o
r
d
i
s
t
r
i
b
u
t
i
o
n
s
a
r
e
m
o
r
e
in
f
lu
en
c
e
d
b
y
th
e
d
a
t
a
,
s
o
th
ey
w
ill
p
r
o
v
i
d
e
m
o
r
e
n
eu
t
r
al
e
s
t
im
a
tes
.
R
esear
ch
o
n
e
s
ti
m
ati
n
g
co
n
ti
n
u
o
u
s
d
is
tr
ib
u
tio
n
p
ar
a
m
eter
s
u
s
i
n
g
a
B
a
y
es
ian
ap
p
r
o
ac
h
to
s
u
r
v
i
v
al
an
al
y
s
is
w
as
ca
r
r
ied
o
u
t
b
y
[
1
3
]
w
h
ic
h
e
x
p
lain
s
t
h
e
u
s
e
o
f
t
h
e
B
a
y
e
s
ian
li
n
ea
r
ex
p
o
n
e
n
tial
lo
s
s
f
u
n
ct
io
n
m
et
h
o
d
in
esti
m
ati
n
g
ex
p
o
n
e
n
tial
d
is
tr
ib
u
tio
n
p
ar
a
m
eter
s
o
n
t
y
p
e
I
ce
n
s
o
r
ed
d
ata
u
s
i
n
g
J
ef
f
r
e
y
’
s
p
r
io
r
.
Fu
r
t
h
er
m
o
r
e,
r
esear
ch
co
n
d
u
c
ted
b
y
[
1
4
]
ex
p
lain
s
th
e
u
s
e
o
f
th
e
B
a
y
esia
n
li
n
ea
r
ex
p
o
n
en
tial
lo
s
s
f
u
n
ct
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n
m
et
h
o
d
in
esti
m
ati
n
g
ex
p
o
n
en
tial
d
is
tr
ib
u
tio
n
p
ar
a
m
eter
s
u
s
in
g
Ga
m
m
a
p
r
io
r
s
.
T
h
e
au
th
o
r
w
is
h
es
to
co
n
d
u
c
t
r
esear
ch
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p
ar
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m
eter
esti
m
at
i
o
n
f
r
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m
a
t
w
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-
p
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m
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ex
p
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en
t
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d
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o
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t
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p
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I
ce
n
s
o
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ed
d
ata
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s
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n
g
th
e
B
a
y
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ian
l
in
ea
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x
p
o
n
en
ti
al
lo
s
s
f
u
n
ctio
n
m
e
th
o
d
.
J
ef
f
r
e
y
’
s
n
o
n
-
in
f
o
r
m
a
tiv
e
p
r
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r
is
t
h
e
p
r
io
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d
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tr
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u
tio
n
th
at
is
u
s
ed
.
T
h
is
is
b
ased
o
n
t
h
e
b
ac
k
g
r
o
u
n
d
t
h
at
w
as p
r
ev
io
u
s
l
y
ex
p
lai
n
ed
.
2.
M
E
T
H
O
D
2
.
1
.
L
inea
r
ex
po
nentia
l lo
s
s
f
un
ct
io
n
L
i
n
ea
r
ex
p
o
n
en
tia
l
lo
s
s
f
u
n
cti
o
n
is
o
n
e
o
f
th
e
lo
s
s
f
u
n
ctio
n
s
u
s
ed
in
s
tati
s
tical
an
al
y
s
is
f
o
r
esti
m
atio
n
an
d
f
o
r
ec
asti
n
g
p
r
o
b
le
m
s
t
h
at
s
h
o
w
e
x
p
o
n
e
n
tial
g
r
o
w
th
o
n
o
n
e
s
id
e
o
f
ze
r
o
an
d
al
m
o
s
t
lin
ea
r
o
n
th
e
o
t
h
er
s
id
e
o
f
ze
r
o
[
1
5
]
.
T
h
e
lin
ea
r
e
x
p
o
n
en
t
ial
f
u
n
c
tio
n
s
h
o
w
s
a
h
ig
h
d
eg
r
ee
o
f
f
le
x
ib
ilit
y
in
m
e
a
s
u
r
i
n
g
est
i
m
a
tio
n
,
b
ec
au
s
e
li
n
ea
r
ex
p
o
n
en
tial
is
ab
le
to
ad
j
u
s
t
v
ar
y
i
n
g
w
ei
g
h
t
s
.
T
h
is
m
et
h
o
d
h
as
b
ee
n
w
id
el
y
u
s
ed
b
y
s
e
v
er
al
r
esear
ch
er
s
,
in
cl
u
d
i
n
g
[
1
6
]
,
[
1
7
]
.
T
h
e
f
o
r
m
u
la
f
o
r
th
e
li
n
ea
r
ex
p
o
n
en
t
ial
lo
s
s
f
u
n
ct
io
n
f
o
r
p
ar
a
m
eter
is
:
(
̂
,
)
=
e
xp
(
(
̂
−
)
)
−
(
̂
−
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−
1
,
≠
0
(
1
)
Usi
n
g
t
h
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li
n
ea
r
ex
p
o
n
e
n
tial
l
o
s
s
f
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n
ctio
n
,
t
h
e
v
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e
o
f
t
h
e
p
o
s
ter
io
r
ex
p
ec
tatio
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f
o
r
p
ar
am
eter
θ,
r
ep
r
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ted
b
y
,
ca
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ex
p
r
ess
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as
(
2
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:
(
(
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=
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(
̂
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(
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(
−
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)
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−
(
̂
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(
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)
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1
(
2
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w
h
e
r
e
a
i
s
a
c
o
n
t
r
o
l
p
a
r
a
m
e
t
e
r
t
h
a
t
s
e
t
s
t
h
e
m
a
g
n
i
t
u
d
e
o
f
t
h
e
d
i
s
c
r
e
p
a
n
c
y
b
e
tw
e
e
n
t
h
e
e
s
t
i
m
a
t
e
d
a
n
d
a
c
t
u
a
l
v
a
l
u
e
s
.
2
.
2
.
P
ri
o
r
J
ef
f
re
y
’
s
No
n
-
i
n
f
o
r
m
ati
v
e
p
r
io
r
d
is
tr
ib
u
tio
n
is
a
co
n
ce
p
t
in
B
a
y
esian
s
tatis
t
ics
t
h
at
r
ef
er
s
t
o
a
p
r
i
o
r
d
is
tr
ib
u
tio
n
u
s
ed
to
d
escr
ib
e
p
r
io
r
k
n
o
w
led
g
e
ab
o
u
t
a
p
ar
ticu
lar
p
ar
am
e
ter
.
A
n
o
n
-
i
n
f
o
r
m
ati
v
e
p
r
io
r
s
ap
p
r
o
ac
h
is
im
p
o
r
tan
t
w
h
e
n
n
o
t
h
av
i
n
g
s
u
f
f
icie
n
t
k
n
o
w
led
g
e
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r
k
ee
p
in
g
th
e
an
a
l
y
s
is
r
es
u
lts
f
r
ee
f
r
o
m
b
ias.
On
e
f
o
r
m
o
f
n
o
n
-
i
n
f
o
r
m
ati
v
e
p
r
io
r
th
at
is
o
f
te
n
u
s
ed
is
t
h
e
J
ef
f
r
e
y
’
s
m
et
h
o
d
[
1
2
]
.
A
s
p
er
t
h
e
J
ef
f
r
e
y
’
s
m
eth
o
d
ap
p
r
o
ac
h
[
1
3
]
,
it
is
r
ec
o
m
m
e
n
d
ed
th
at
th
e
p
r
ev
io
u
s
d
i
s
tr
ib
u
t
io
n
h
a
v
e
a
s
q
u
ar
e
r
o
o
t
o
f
th
e
Fis
h
er
in
f
o
r
m
at
io
n
.
Fis
h
er
’
s
p
ar
a
m
eter
f
o
r
in
f
o
r
m
atio
n
v
al
u
e
is
d
ef
in
ed
as
(
3
)
:
(
)
=
−
[
2
ln
(
(
)
)
2
]
(
3
)
T
h
en
,
a
p
r
io
r
d
is
tr
ib
u
tio
n
ca
n
b
e
f
o
r
m
u
lated
f
r
o
m
Fi
s
h
er
i
n
f
o
r
m
at
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
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o
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tr
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B
a
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s
esti
ma
tio
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f a
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p
a
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mete
r
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p
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l d
is
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imp
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ta
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(
A
r
d
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r
n
ia
w
a
n
)
1445
(
)
∝
√
(
)
(
4
)
w
h
er
e,
f
(
t)
is
t
h
e
p
r
o
b
ab
ilit
y
d
en
s
it
y
f
u
n
ctio
n
(
P
DF)
o
f
a
t
w
o
-
p
ar
a
m
eter
ex
p
o
n
e
n
tial d
i
s
tr
ib
u
tio
n
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Ana
ly
s
is
o
f
ba
y
es e
s
t
i
m
a
t
io
n
~
(
,
)
ca
n
b
e
u
s
ed
to
r
ep
r
esen
t
th
e
s
u
r
v
i
v
i
n
g
o
b
s
er
v
atio
n
d
ata,
w
h
ich
ar
e
s
u
p
p
o
s
ed
to
b
e
1
,
2
,
…
,
f
r
o
m
a
r
an
d
o
m
v
ar
iab
le
T
o
f
s
ize
w
i
th
an
e
x
p
o
n
en
t
ial
d
is
tr
ib
u
tio
n
w
it
h
p
ar
am
e
ter
s
an
d
.
As
p
er
r
ef
er
en
ce
L
ee
a
n
d
W
an
g
[
1
8
]
,
th
e
P
DF
s
er
v
e
s
as
a
to
o
l
to
g
au
g
e
th
e
L
ik
el
ih
o
o
d
th
at
a
n
i
n
d
iv
id
u
al
w
o
u
ld
en
co
u
n
ter
a
s
p
ec
if
ic
e
v
e
n
t d
u
r
i
n
g
t
h
e
ti
m
e
f
r
a
m
e
to
(
+
∆
)
.
So
,
th
e
P
DF
is
[
1
9
]
.
(
;
;
)
=
{
−
(
−
)
;
≥
,
>
0
0
;
<
0
(
5
)
I
n
f
o
r
m
in
g
t
h
e
L
i
k
eli
h
o
o
d
f
u
n
ctio
n
,
a
s
u
r
v
i
v
al
f
u
n
ctio
n
f
o
r
m
u
la
is
n
ee
d
ed
.
A
cc
o
r
d
in
g
t
o
T
o
lb
a
[
2
0
]
,
th
e
s
u
r
v
iv
al
f
u
n
ct
io
n
is
a
s
tati
s
tic
al
an
al
y
s
is
u
s
ed
to
u
n
d
er
s
ta
n
d
p
h
en
o
m
e
n
a
r
elate
d
to
ti
m
e.
I
n
(
6
)
is
th
e
s
u
r
v
iv
al
f
u
n
ctio
n
o
f
t
h
e
t
w
o
-
p
ar
a
m
e
ter
ex
p
o
n
en
t
ial
d
is
tr
ib
u
t
io
n
.
(
)
=
−
(
−
)
(
6
)
T
h
e
r
an
d
o
m
v
ar
iab
le
f
r
o
m
t
y
p
e
I
ce
n
s
o
r
ed
d
ata
h
as
t
h
e
f
o
llo
w
i
n
g
L
ik
el
ih
o
o
d
f
u
n
ctio
n
af
ter
d
er
iv
in
g
t
h
e
s
u
r
v
iv
al
f
u
n
c
tio
n
f
o
r
m
u
la
[
2
1
]
.
(
)
=
∏
(
)
(
)
1
−
=
1
(
7
)
(
)
=
∏
(
−
(
−
)
)
=
1
(
−
(
−
)
)
1
−
(
8
)
(
)
=
∑
=
1
−
∑
(
=
1
−
)
(
9
)
T
o
g
en
er
ate
th
e
L
ik
e
lih
o
o
d
f
u
n
ctio
n
,
u
s
e
(
7
)
.
I
t
is
th
er
ef
o
r
e
p
o
s
s
ib
le
to
d
eter
m
in
e
th
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
,
w
h
ic
h
is
d
en
o
ted
b
y
(
|
)
.
3
.
1
.
1
.
Ana
ly
s
is
o
f
ba
y
es e
s
t
im
a
t
io
n w
it
h a
s
s
u
m
i
ng
bo
t
h pa
ra
m
et
er
s
a
re
v
a
ria
ble
T
h
e
f
o
r
m
u
la
f
o
r
th
e
L
i
k
eli
h
o
o
d
f
u
n
ctio
n
h
as
b
ee
n
o
b
tain
ed
,
th
en
t
h
e
n
at
u
r
al
lo
g
ar
it
h
m
o
f
th
e
L
i
k
eli
h
o
o
d
f
u
n
ctio
n
w
i
ll b
e
ca
lcu
lated
.
(
(
)
)
=
(
−
(
−
)
)
(
10
)
(
(
)
)
=
(
)
−
(
−
)
(1
1
)
T
h
e
r
esu
lts
o
f
(
(
)
)
w
ill
t
h
en
b
e
u
s
ed
to
d
eter
m
i
n
e
t
h
e
Fi
s
h
er
’
s
i
n
f
o
r
m
atio
n
v
al
u
e
o
b
tain
ed
f
r
o
m
t
h
e
f
ir
s
t
an
d
s
ec
o
n
d
d
er
iv
ati
v
es o
f
(
(
)
)
.
So
,
Fis
h
er
’
s
i
n
f
o
r
m
atio
n
v
al
u
e
w
i
ll b
e
a
d
eter
m
i
n
an
t
[
2
2
]
.
(
)
=
−
[
2
(
(
)
)
2
2
(
(
)
)
2
(
(
)
)
2
(
(
)
)
2
]
(1
2
)
(
)
=
−
[
−
1
2
1
1
0
]
(1
3
)
B
ased
o
n
th
e
Fis
h
er
’
s
i
n
f
o
r
m
atio
n
m
atr
i
x
ac
co
r
d
in
g
to
(
4
)
w
i
th
r
ef
er
e
n
ce
to
(
1
2
)
,
th
e
f
o
r
m
o
f
th
e
p
r
io
r
d
is
tr
ib
u
tio
n
ca
n
b
e
d
escr
ib
ed
a
s
(1
4
)
an
d
(
1
5
)
:
(
)
∝
√
(
)
(1
4
)
(
)
∝
1
(1
5
)
T
h
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
in
th
e
B
a
y
e
s
t
h
eo
r
e
m
is
p
r
o
d
u
ce
d
b
y
co
m
b
in
i
n
g
t
h
e
J
ef
f
r
e
y
’
s
p
r
io
r
d
is
tr
ib
u
tio
n
w
h
ic
h
w
as
p
r
ev
io
u
s
l
y
co
m
p
u
ted
w
it
h
th
e
L
i
k
eli
h
o
o
d
f
u
n
c
tio
n
[
2
3
]
.
A
B
ay
e
s
ian
ap
p
r
o
ac
h
f
o
u
n
d
atio
n
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
22
,
No
.
6
,
Dec
em
b
er
20
24
:
1
4
4
3
-
1
449
1446
s
tatis
t
ical
in
f
er
en
ce
w
ill
b
e
th
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
[
2
4
]
.
A
cc
o
r
d
in
g
to
Z
h
a
n
g
an
d
Gao
[
2
5
]
,
th
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
d
en
o
ted
b
y
(
|
)
h
as
(
1
6
)
to
(
1
8
)
:
(
|
)
=
(
)
.
(
)
∫
∫
(
)
.
(
)
∞
0
∞
0
(1
6
)
(
|
)
=
∑
=
1
−
∑
(
=
1
−
)
.
(
1
)
∫
∫
∑
=
1
−
∑
(
=
1
−
)
.
(
1
)
∞
0
∞
0
(1
7
)
(
|
)
=
∑
=
1
−
∑
(
=
1
−
)
∫
∑
=
1
−
∑
=
1
(
∫
∞
0
)
∞
0
=
0
(1
8
)
T
h
e
r
e
s
u
l
t
o
f
t
h
e
i
n
t
eg
r
a
l
o
v
e
r
th
e
p
a
r
am
e
t
e
r
μ
is
in
f
in
i
ty
,
s
o
t
h
a
t
i
f
t
h
e
i
n
t
eg
r
a
l
o
v
e
r
i
s
m
u
l
ti
p
l
i
e
d
b
y
in
f
in
ity
i
t
w
il
l
s
t
i
ll
p
r
o
d
u
c
e
an
i
n
f
i
n
i
t
e
v
a
l
u
e
.
T
h
is
r
e
s
u
lt
s
in
th
e
p
o
s
t
e
r
io
r
d
i
s
t
r
i
b
u
t
i
o
n
e
q
u
at
i
o
n
b
e
i
n
g
z
e
r
o
.
S
o
,
p
a
r
am
e
t
e
r
e
s
t
im
at
i
o
n
u
s
i
n
g
t
h
e
l
in
e
a
r
ex
p
o
n
en
t
i
al
l
o
s
s
f
u
n
c
ti
o
n
m
et
h
o
d
u
s
in
g
th
e
J
e
f
f
r
ey
’
s
(
)
p
r
i
o
r
c
a
n
n
o
t
b
e
a
p
p
l
i
e
d
.
3
.
1
.
2
.
Ana
ly
s
is
o
f
ba
y
es e
s
t
im
a
t
io
n w
it
h a
s
s
u
m
i
ng
pa
ra
m
et
er
is
co
ns
t
a
nt
a
nd
pa
ra
m
et
er
is
v
a
ria
ble
T
h
e
f
ir
s
t a
n
d
s
ec
o
n
d
d
er
iv
ati
v
es o
f
(
(
)
)
ar
e
as
(1
9
)
:
2
(
(
)
)
2
=
0
(1
9
)
B
ased
o
n
th
e
r
esu
lts
o
f
t
h
e
s
ec
o
n
d
d
er
iv
ativ
e
o
f
t
h
e
f
u
n
ctio
n
(
(
)
)
o
n
th
e
p
ar
a
m
eter
,
th
e
Fis
h
er
in
f
o
r
m
atio
n
v
al
u
e
f
o
r
th
e
p
ar
a
m
eter
μ
ca
n
b
e
d
escr
ib
ed
as
(
20
)
an
d
(
2
1
)
:
(
)
=
−
(
2
(
(
)
)
2
)
(
20
)
(
)
=
0
(2
1
)
T
h
e
ca
lcu
latio
n
r
es
u
lts
in
(
2
2
)
s
h
o
w
t
h
at
th
e
Fi
s
h
er
i
n
f
o
r
m
atio
n
v
alu
e
is
ze
r
o
,
s
o
th
e
p
ar
a
m
eter
esti
m
at
io
n
ca
n
n
o
t b
e
ap
p
li
ed
ass
u
m
i
n
g
t
h
e
p
ar
am
eter
is
co
n
s
ta
n
t a
n
d
t
h
e
p
ar
am
eter
is
v
ar
iab
le
.
3
.
1
.
3
.
Ana
ly
s
is
o
f
ba
y
es e
s
t
im
a
t
io
n w
it
h a
s
s
u
m
i
ng
pa
ra
m
et
er
is
v
a
ria
ble a
nd
pa
ra
m
et
er
is
co
s
t
a
nt
T
h
e
f
ir
s
t a
n
d
s
ec
o
n
d
d
er
iv
ati
v
es o
f
(
(
)
)
ar
e
as
(2
2
)
:
2
(
(
)
)
2
=
−
1
2
(2
2
)
B
ased
o
n
th
e
r
esu
lts
o
f
t
h
e
s
ec
o
n
d
d
er
iv
ativ
e
o
f
t
h
e
f
u
n
ctio
n
(
(
)
)
o
n
th
e
p
ar
am
eter
,
th
e
Fis
h
e
r
in
f
o
r
m
atio
n
v
al
u
e
f
o
r
th
e
p
ar
a
m
eter
μ
ca
n
b
e
d
escr
ib
ed
as
(2
3
)
an
d
(
2
4
)
:
(
)
=
−
(
2
(
(
)
)
2
)
(2
3
)
(
)
=
1
2
(2
4
)
I
n
ac
co
r
d
an
ce
w
ith
t
h
e
v
al
u
e
o
f
th
e
Fis
h
er
in
f
o
r
m
at
io
n
m
atr
ix
o
b
tain
ed
in
(
2
5
)
,
th
e
J
ef
f
r
ey
’
s
p
r
io
r
d
is
tr
ib
u
tio
n
(
)
ca
n
b
e
d
eter
m
i
n
ed
as
(2
5
)
:
(
)
∝
1
(2
5
)
Nex
t,
d
eter
m
i
n
e
t
h
e
f
o
r
m
u
la
f
o
r
th
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
.
(
|
)
=
(
)
.
(
)
∫
(
)
.
(
)
∞
0
(2
6
)
(
|
)
=
∑
=
1
−
∑
(
=
1
−
)
.
(
1
)
∫
∑
=
1
−
∑
(
=
1
−
)
.
(
1
)
∞
0
(2
7
)
(
|
)
=
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∫
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∞
0
(2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
B
a
ye
s
esti
ma
tio
n
o
f a
tw
o
-
p
a
r
a
mete
r
ex
p
o
n
en
tia
l d
is
tr
ib
u
tio
n
a
n
d
its
imp
leme
n
ta
tio
n
(
A
r
d
i Ku
r
n
ia
w
a
n
)
1447
E
s
ti
m
a
tin
g
t
h
e
p
r
ev
io
u
s
l
y
u
n
k
n
o
w
n
p
ar
a
m
eter
co
m
e
s
n
e
x
t
af
ter
o
b
tain
i
n
g
t
h
e
p
o
s
ter
io
r
d
is
tr
ib
u
tio
n
.
I
n
t
h
i
s
r
esear
ch
,
th
e
B
a
y
esia
n
li
n
ea
r
ex
p
o
n
en
t
ial
lo
s
s
f
u
n
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n
m
et
h
o
d
w
ill
b
e
u
s
ed
to
esti
m
ate
th
e
p
ar
a
m
eter
.
T
h
e
lo
s
s
f
u
n
ctio
n
(
̂
;
)
is
d
escr
ib
ed
as
(2
9
)
:
(
̂
;
)
=
(
(
̂
−
)
)
−
(
̂
−
)
−
1
,
≠
0
(2
9
)
I
n
a
t
w
o
-
p
ar
a
m
eter
e
x
p
o
n
en
ti
al
d
is
tr
ib
u
tio
n
,
t
h
e
p
o
s
ter
io
r
ex
p
ec
tatio
n
v
al
u
e
(
)
o
f
t
h
e
lo
s
s
f
u
n
ctio
n
i
n
(
3
0
)
is
m
i
n
i
m
ized
to
p
r
o
d
u
ce
th
e
B
ay
esia
n
li
n
ea
r
ex
p
o
n
e
n
tial
esti
m
at
io
n
o
f
th
e
p
ar
a
m
eter
θ.
T
h
is
p
r
o
ce
s
s
is
ex
p
lain
ed
as
(
30
)
an
d
(
3
1
)
:
(
(
̂
,
)
)
=
[
(
̂
−
)
−
(
̂
−
)
−
1
]
(
30
)
(
(
̂
,
)
)
=
̂
.
(
−
)
−
(
̂
−
(
)
)
−
1
(3
1
)
T
h
e
n
ex
t
s
tep
is
to
m
i
n
i
m
ize
(
3
2
)
b
y
f
i
n
d
i
n
g
t
h
e
f
ir
s
t
d
er
i
v
at
iv
e
o
f
̂
th
e
n
s
et
tin
g
it
to
ze
r
o
.
So
,
w
e
w
i
ll
g
e
t
a
B
ay
e
s
ian
l
in
ea
r
e
x
p
o
n
en
t
ial
es
ti
m
ato
r
o
f
t
h
e
p
ar
a
m
eter
as
(3
2
)
-
(3
4
)
:
(
(
(
̂
;
)
)
)
̂
=
0
(3
2
)
(
̂
.
(
−
)
−
(
̂
−
(
)
)
−
1
)
̂
=
0
(3
3
)
̂
=
−
1
(
(
(
−
)
)
)
(3
4
)
Fro
m
th
i
s
esti
m
ato
r
,
th
e
v
al
u
e
o
f
(
−
)
is
th
e
n
ca
lc
u
lated
w
h
ich
i
s
th
e
p
o
s
ter
io
r
ex
p
ec
ted
v
al
u
e
o
f
−
s
o
th
at
it c
a
n
b
e
d
escr
ib
ed
as
(3
5
)
an
d
(
3
6
)
:
(
−
)
=
∫
−
.
∞
0
(
|
)
(3
5
)
(
−
)
=
∫
−
(
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∫
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∞
0
)
∞
0
(3
6
)
T
h
u
s
,
t
h
e
p
ar
a
m
eter
es
ti
m
ato
r
f
r
o
m
th
e
t
w
o
-
p
ar
a
m
eter
ex
p
o
n
en
tial
d
is
tr
ib
u
t
io
n
u
s
i
n
g
t
h
e
B
ay
e
s
ia
n
li
n
ea
r
ex
p
o
n
en
t
ial
m
e
th
o
d
is
as
(3
7
)
:
̂
=
−
1
(
(
∫
−
.
∞
0
(
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∫
(
∑
)
−
1
=
1
−
∑
(
=
1
−
)
∞
0
)
)
)
(3
7
)
3
.
2
.
I
m
ple
m
e
nta
t
io
n o
f
ba
y
e
s
esti
m
a
t
io
n a
na
ly
s
is
Af
ter
o
b
tain
i
n
g
p
ar
a
m
eter
es
ti
m
ate
s
f
r
o
m
t
h
e
t
w
o
-
p
ar
a
m
eter
ex
p
o
n
en
tial
d
is
tr
ib
u
tio
n
u
s
i
n
g
t
h
e
B
ay
e
s
ian
li
n
ea
r
ex
p
o
n
e
n
tial
lo
s
s
f
u
n
ctio
n
ap
p
r
o
ac
h
b
ased
o
n
J
ef
f
r
e
y
’
s
p
r
io
r
an
d
th
e
a
s
s
u
m
p
tio
n
s
t
h
at
ar
e
m
et,
n
a
m
e
l
y
th
e
a
s
s
u
m
p
tio
n
p
ar
a
m
eter
v
ar
iab
le
an
d
t
h
e
p
ar
am
eter
co
n
s
id
er
ed
co
n
s
ta
n
t.
Nex
t,
t
h
e
r
es
u
lt
s
o
f
th
ese
p
ar
a
m
eter
esti
m
ates
w
il
l
b
e
a
p
p
li
ed
to
r
ea
l
d
ata.
T
h
e
d
ata
th
at
w
i
ll
b
e
u
s
ed
is
s
ec
o
n
d
ar
y
d
ata
in
th
e
f
o
r
m
o
f
d
ata
o
n
h
o
w
lo
n
g
e
m
p
lo
y
ee
s
h
av
e
w
o
r
k
ed
b
ef
o
r
e
th
e
y
ex
p
er
ie
n
ce
d
attr
itio
n
i
n
2
0
2
1
.
T
h
is
d
ata
w
a
s
o
b
tain
ed
f
r
o
m
th
e
K
a
g
g
le.
co
m
w
eb
s
ite
e
n
titl
ed
“
I
B
M
H
R
An
al
y
tics
E
m
p
lo
y
ee
A
ttri
tio
n
&
P
er
f
o
r
m
a
n
ce
”
.
I
n
th
is
s
t
u
d
y
,
a
s
a
m
p
le
o
f
5
0
e
m
p
lo
y
ee
s
w
as
ta
k
e
n
w
it
h
a
ce
n
s
o
r
s
h
ip
li
m
it
b
ased
o
n
a
g
e,
n
a
m
el
y
5
8
y
ea
r
s
.
Af
ter
d
eter
m
in
i
n
g
th
e
ce
n
s
o
r
s
h
ip
li
m
it,
o
u
t
o
f
5
0
em
p
lo
y
ee
s
w
h
o
co
u
ld
b
e
o
b
s
er
v
ed
,
th
er
e
w
er
e
4
8
em
p
lo
y
ee
s
.
T
esti
n
g
th
e
d
ata
d
is
tr
ib
u
tio
n
is
th
e
f
ir
s
t
ac
tio
n
th
a
t
ca
n
b
e
d
o
n
e
b
ef
o
r
e
esti
m
ati
n
g
p
ar
am
eter
s
u
s
i
n
g
ac
t
u
al
d
ata.
T
h
is
s
t
u
d
y
e
m
p
lo
y
ed
a
tw
o
-
p
ar
a
m
eter
ex
p
o
n
e
n
tial d
at
a
d
is
tr
ib
u
tio
n
w
it
h
t
h
e
f
o
llo
w
i
n
g
h
y
p
o
t
h
esi
s
:
0
=
t
h
e
d
ata
f
o
llo
w
a
t
w
o
-
p
ar
a
m
et
er
ex
p
o
n
en
tial d
is
tr
ib
u
tio
n
.
1
=
t
h
e
d
ata
d
o
es n
o
t f
o
llo
w
a
t
w
o
-
p
ar
a
m
eter
ex
p
o
n
e
n
tial d
i
s
tr
ib
u
tio
n
.
B
y
u
s
i
n
g
t
h
e
test
i
n
g
cr
iter
ia
=
0
.
05
,
th
e
d
ec
is
io
n
0
w
ill
b
e
r
ej
ec
ted
if
th
e
−
<
.
T
h
e
r
esu
lt
s
o
f
t
h
e
d
is
tr
ib
u
tio
n
s
u
ita
b
ilit
y
te
s
t o
b
tain
ed
a
−
o
f
0
.
4
3
3
7
7
.
T
h
is
s
h
o
w
s
t
h
e
−
>
0
.
05
,
s
o
th
e
d
ec
is
io
n
is
to
ac
ce
p
t
0
.
So
,
it
ca
n
b
e
co
n
cl
u
d
ed
th
a
t
t
h
e
d
ata
o
n
e
m
p
lo
y
ee
le
n
g
th
o
f
w
o
r
k
i
n
2
0
2
1
f
o
llo
w
s
a
t
w
o
-
p
ar
a
m
eter
ex
p
o
n
en
t
ial
d
is
tr
ib
u
t
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
22
,
No
.
6
,
Dec
em
b
er
20
24
:
1
4
4
3
-
1
449
1448
Af
ter
k
n
o
w
i
n
g
t
h
e
s
h
ap
e
o
f
th
e
d
ata
d
is
tr
ib
u
tio
n
,
th
e
n
ex
t
s
t
ep
is
to
d
eter
m
i
n
e
th
e
e
s
ti
m
at
ed
v
alu
e
o
f
th
e
p
ar
am
eter
in
t
h
e
d
ata
o
n
e
m
p
lo
y
ee
le
n
g
th
o
f
w
o
r
k
in
2
0
2
1
.
B
ased
o
n
th
e
ass
u
m
p
tio
n
t
h
at
th
e
p
ar
am
eter
i
s
co
n
s
tan
t
a
n
d
th
e
p
ar
am
eter
i
s
v
ar
iab
le,
t
h
e
es
ti
m
ated
v
alu
e
o
f
t
h
e
p
ar
am
et
er
w
ill
b
e
ta
k
e
n
f
r
o
m
min
(
)
or
1
.
So
,
it
ca
n
b
e
s
aid
t
h
at
t
h
e
est
i
m
a
ted
v
al
u
e
o
f
th
e
p
ar
am
eter
is
t
h
e
s
a
m
e
a
s
t
h
e
s
m
al
lest
T
v
alu
e
f
r
o
m
t
h
e
d
ata.
T
h
e
s
m
alle
s
t
T
v
al
u
e
f
r
o
m
e
m
p
lo
y
ee
len
g
t
h
o
f
w
o
r
k
d
ata
i
n
2
0
2
1
is
1
y
ea
r
.
T
h
u
s
,
i
t
ca
n
b
e
s
aid
th
at
t
h
e
p
ar
am
eter
’
s
es
ti
m
ated
v
al
u
e
is
1
.
T
h
e
d
ata
d
is
tr
ib
u
tio
n
h
as
b
ee
n
m
et
an
d
t
h
e
esti
m
ated
v
alu
e
o
f
th
e
p
ar
a
m
eter
h
as
b
ee
n
d
et
er
m
in
ed
.
Nex
t,
t
h
e
v
al
u
e
o
f
a
is
d
eter
m
i
n
ed
b
ased
o
n
th
e
e
s
ti
m
atio
n
r
es
u
lt
s
t
h
at
h
a
v
e
b
ee
n
o
b
tai
n
ed
.
T
h
is
i
s
d
o
n
e
b
y
t
ak
i
n
g
t
h
e
v
al
u
e
o
f
a
th
at
is
clo
s
est
to
th
e
av
er
ag
e
v
a
lu
e
o
f
all
̂
ca
lcu
latio
n
r
esu
lt
s
.
T
h
e
v
alu
e
o
f
a
h
as
t
h
e
co
n
d
itio
n
th
at
≠
0
.
T
h
e
v
alu
e
o
f
a
th
at
w
ill
b
e
u
s
ed
is
a
=
-
0
.
2
5
;
-
0
.
5
0
;
-
0
.
7
5
;
-
1
an
d
a
=0
.
2
5
;
0
.
5
0
;
0
.
7
5
;
1
.
T
h
e
av
er
ag
e
o
f
all
̂
v
alu
e
s
i
s
0
.
1
2
6
3
1
6
.
So
,
th
e
v
al
u
e
o
f
̂
th
at
is
clo
s
e
s
t
to
th
e
a
v
er
a
g
e
v
alu
e
is
̂
u
s
in
g
t
h
e
v
alu
e
a
=0
.
2
5
.
A
s
id
e
f
r
o
m
th
a
t,
it
is
ev
id
en
t
th
at
̂
in
cr
ea
s
es
w
it
h
d
ec
r
ea
s
in
g
a
v
alu
e.
O
n
th
e
o
th
er
h
an
d
,
̂
w
il
l
h
a
v
e
a
s
m
aller
v
alu
e
if
a
n
is
h
i
g
h
er
.
S
in
ce
t
h
er
e
w
ill
b
e
less
o
f
a
d
i
s
cr
ep
an
c
y
b
et
w
ee
n
th
e
e
s
ti
m
ated
a
n
d
ac
tu
al
v
a
lu
e
s
,
an
i
n
cr
ea
s
ed
v
al
u
e
o
f
a
w
ill
y
ield
s
m
o
r
e
ac
c
u
r
ate
esti
m
atio
n
r
es
u
lt
s
.
On
ce
t
h
e
v
al
u
e
o
f
a
is
k
n
o
w
n
,
th
e
esti
m
ated
v
alu
e
o
f
p
ar
am
eter
ca
n
b
e
ca
lcu
lated
.
B
ased
o
n
th
e
ca
lcu
latio
n
r
esu
l
ts
,
th
e
e
s
ti
m
at
ed
p
ar
am
eter
w
i
th
a
v
a
lu
e
o
f
a
=0
.
2
5
an
d
̂
=1
in
th
e
e
m
p
lo
y
ee
len
g
t
h
o
f
w
o
r
k
d
ata
in
2
0
2
1
is
0
.
1
8
8
6
0
5
.
T
h
e
av
er
ag
e
len
g
t
h
o
f
ti
m
e
e
m
p
l
o
y
ee
s
h
av
e
w
o
r
k
ed
is
6
.
2
9
4
2
7
y
ea
r
s
.
T
h
is
s
h
o
ws
th
at
e
m
p
lo
y
ee
s
te
n
d
to
e
x
p
er
ien
ce
attr
itio
n
a
f
ter
w
o
r
k
i
n
g
f
o
r
a
r
elativ
el
y
lo
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[
1
9
]
J.
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.
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2
3
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2
4
]
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.
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2
5
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.
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B
I
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RAP
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Ar
d
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tatisti
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s)
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Un
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a
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:
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a
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id
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