<s>
In	O
statistics	O
,	O
the	O
Lepage	B-General_Concept
test	I-General_Concept
is	O
an	O
exactly	O
distribution-free	B-General_Concept
test	I-General_Concept
(	O
nonparametric	B-General_Concept
test	I-General_Concept
)	O
for	O
jointly	O
monitoring	O
the	O
location	O
(	O
central	O
tendency	O
)	O
and	O
scale	O
(	O
variability	O
)	O
in	O
two-sample	O
treatment	O
versus	O
control	O
comparisons	O
.	O
</s>
<s>
This	O
is	O
one	O
of	O
the	O
most	O
famous	O
rank	O
tests	O
for	O
the	O
two-sample	B-Algorithm
location-scale	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
Lepage	B-General_Concept
test	I-General_Concept
statistic	O
is	O
the	O
squared	O
Euclidean	O
distance	O
of	O
standardized	O
Wilcoxon	B-General_Concept
rank-sum	I-General_Concept
test	I-General_Concept
for	O
location	O
and	O
the	O
standardized	O
Ansari	O
–	O
Bradley	O
test	O
for	O
scale	O
.	O
</s>
<s>
The	O
Lepage	B-General_Concept
test	I-General_Concept
was	O
first	O
introduced	O
by	O
Yves	O
Lepage	O
in	O
1971	O
in	O
a	O
paper	O
in	O
Biometrika	O
.	O
</s>
<s>
The	O
details	O
may	O
be	O
found	O
in	O
the	O
book	O
:	O
Nonparametric	B-General_Concept
statistical	O
tests	O
:	O
A	O
computational	O
approach	O
.	O
</s>
<s>
Dr.	O
Amitava	O
Mukherjee	O
and	O
Dr.	O
Marco	O
Marozzi	O
introduced	O
a	O
class	O
of	O
percentile	O
modified	O
version	O
of	O
the	O
Lepage	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
An	O
alternative	O
to	O
the	O
Lepage-type	O
tests	O
is	O
known	O
as	O
the	O
Cucconi	B-General_Concept
test	I-General_Concept
proposed	O
by	O
Odoardo	O
Cucconi	O
in	O
1968	O
.	O
</s>
<s>
Practitioners	O
can	O
apply	O
the	O
Lepage	B-General_Concept
test	I-General_Concept
using	O
the	O
pLepage	O
function	O
of	O
the	O
contributory	O
package	O
NSM3	O
,	O
built	O
under	O
R	O
software	O
.	O
</s>
<s>
Andreas	O
Schulz	O
and	O
Markus	O
Neuhäuser	O
also	O
provided	O
detailed	O
R	O
code	O
for	O
computation	O
of	O
test	O
statistic	O
and	O
p-value	O
of	O
the	O
Lepage	B-General_Concept
test	I-General_Concept
for	O
the	O
users	O
.	O
</s>
<s>
In	O
a	O
classical	O
development	O
,	O
in	O
2012	O
,	O
Amitava	O
Mukherjee	O
,	O
an	O
Indian	O
statistician	O
,	O
and	O
Subhabrata	O
Chakraborti	O
,	O
an	O
American	O
statistician	O
of	O
Indian	O
origin	O
,	O
introduced	O
a	O
distribution-free	B-General_Concept
Shewhart-type	O
Phase-II	O
monitoring	O
scheme	O
(	O
control	B-General_Concept
chart	I-General_Concept
)	O
for	O
simultaneously	O
monitoring	O
of	O
location	O
and	O
scale	O
parameter	O
of	O
a	O
process	O
using	O
a	O
test	O
sample	O
of	O
fixed	O
size	O
,	O
when	O
a	O
reference	O
sample	O
of	O
sufficiently	O
large	O
size	O
is	O
available	O
from	O
an	O
in-control	O
population	O
.	O
</s>
<s>
Later	O
in	O
2015	O
,	O
the	O
same	O
statisticians	O
along	O
with	O
Shovan	O
Chowdhury	O
,	O
proposed	O
a	O
distribution-free	B-General_Concept
CUSUM-type	O
Phase-II	O
monitoring	O
scheme	O
based	O
on	O
the	O
Lepage	O
statistic	O
.	O
</s>
<s>
In	O
2017	O
,	O
Mukherjee	O
further	O
designed	O
an	O
EWMA-type	O
distribution-free	B-General_Concept
Phase-II	O
monitoring	O
scheme	O
for	O
joint	O
monitoring	O
of	O
location	O
and	O
scale	O
.	O
</s>
<s>
In	O
the	O
same	O
year	O
,	O
Mukherjee	O
,	O
with	O
Marco	O
Marozzi	O
,	O
an	O
Italian	O
statistician	O
known	O
for	O
promoting	O
the	O
Cucconi	B-General_Concept
test	I-General_Concept
,	O
came	O
together	O
to	O
design	O
Circular-Grid	O
Lepage	O
chart	O
–	O
a	O
new	O
type	O
of	O
joint	O
monitoring	O
scheme	O
.	O
</s>
<s>
In	O
2005	O
,	O
František	O
Rublìk	O
introduced	O
the	O
multisample	O
version	O
of	O
the	O
original	O
two-sample	O
Lepage	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
This	O
work	O
recently	O
emerge	O
as	O
the	O
motivation	O
behind	O
the	O
proposal	O
of	O
the	O
Phase-I	O
distribution-free	B-General_Concept
Shewhart-type	O
control	B-General_Concept
chart	I-General_Concept
for	O
joint	O
monitoring	O
of	O
location	O
and	O
scale	O
.	O
</s>
