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```Statistics::Basic(3)  User Contributed Perl Documentation Statistics::Basic(3)

NAME
Statistics::Basic - A collection	of very	basic statistics modules

SYNOPSIS
use Statistics::Basic qw(:all);

These actually return objects, not numbers.  The	objects	will
interpolate as nicely formated numbers (using Number::Format).  Or the
actual number will be returned when the object is used as a number.

my \$median =	median(	1,2,3 );
my \$mean   =	mean(  [1,2,3]); # array refs are ok too

my \$variance	= variance( 1,2,3 );
my \$stddev	= stddev(   1,2,3 );

Although	passing	unblessed numbers and array refs to these functions
works, it's sometimes better to pass vector objects so the objects can
reuse calculated	values.

my \$v1	= \$mean->query_vector;
my \$variance	= variance( \$v1	);
my \$stddev	= stddev(   \$v1	);

Here, the mean used by the variance and the variance used by the
standard	deviation will not need	to be recalculated.  Now consider
these two calculations.

my \$covariance  = covariance(  [1 ..	3], [1 .. 3] );
my \$correlation = correlation( [1 ..	3], [1 .. 3] );

The covariance above would need to be recalculated by the correlation
when these functions are	called this way.  But, if we instead built
vectors first, that wouldn't happen:

# \$v1 is defined above
my \$v2  = vector(1,2,3);
my \$cov = covariance(  \$v1, \$v2 );
my \$cor = correlation( \$v1, \$v2 );

Now \$cor	can reuse the variance calculated in \$cov.

All of the functions above return objects that interpolate or evaluate
as a single string or as	a number.  Statistics::Basic::LeastSquareFit
and Statistics::Basic::Mode are different:

my \$unimodal	  = mode(1,2,3,3);
my \$multimodal = mode(1,2,3);

print "The modes are: \$unimodal and \$multimodal.\n";
print "The first is multimodal... " if \$unimodal->is_multimodal;
print "The second is	multimodal.\n" if \$multimodal->is_multimodal;

In the first case, \$unimodal will interpolate as	a string and function
correctly as a number.  However,	in the second case, trying to use
\$multimodal as a	number will "croak" an error --	it still interpolates
fine though.

my \$lsf = leastsquarefit(\$v1, \$v2);

This \$lsf will interpolate fine,	showing	"LSF( alpha: \$alpha, beta:
\$beta )", but it	will "croak" if	you try	to use the object as a number.

my \$v3	      =	\$multimodal->query;
my (\$alpha, \$beta) =	\$lsf->query;
my \$average	      =	\$mean->query;

All of the objects allow	you to explicitly query, if you're not in the

\$mode->query,
\$median->query,
\$stddev->query,
);

SHORTCUTS
The following shortcut functions	can be used in place of	calling	the
module's	"new()"	method directly.

They all	take either array refs or lists	as arguments, with the
exception of the	shortcuts that need two	vectors	to process (e.g.
Statistics::Basic::Correlation).

vector()
Returns a Statistics::Basic::Vector object.	Arguments to
"vector()" can be any of: an	array ref, a list of numbers, or a
blessed vector object.  If passed a blessed vector object, vector
will	just return the	vector passed in.

mean() average()	avg()
Returns a Statistics::Basic::Mean object.  You can choose to	call
"mean()" as "average()" or "avg()".	Arguments can be any of: an
array ref, a	list of	numbers, or a blessed vector object.

median()
Returns a Statistics::Basic::Median object.	Arguments can be any
of: an array	ref, a list of numbers,	or a blessed vector object.

mode()
Returns a Statistics::Basic::Mode object.  Arguments	can be any of:
an array ref, a list	of numbers, or a blessed vector	object.

variance() var()
Returns a Statistics::Basic::Variance object.  You can choose to
call	"variance()" as	"var()".  Arguments can	be any of: an array
ref,	a list of numbers, or a	blessed	vector object.	If you will
also	be calculating the mean	of the same list of numbers it's
recommended to do this:

my \$vec	= vector(1,2,3);
my \$mean	= mean(\$vec);
my \$var	= variance(\$vec);

This	would also work:

my \$mean	= mean(1,2,3);
my \$var	= variance(\$mean->query_vector);

This	will calculate the same	mean twice:

my \$mean	= mean(1,2,3);
my \$var	= variance(1,2,3);

If you really only need the variance, ignore	the above and this is
fine:

my \$variance = variance(1,2,3,4,5);

stddev()
Returns a Statistics::Basic::StdDev object.	Arguments can be any
of: an array	ref, a list of numbers,	or a blessed vector object.
Pass	a vector object	to "stddev()" to avoid recalculating the
variance and	mean if	applicable (see	"variance()").

covariance() cov()
Returns a Statistics::Basic::Covariance object.  Arguments to
"covariance()" or "cov()" must be array ref or vector objects.
There must be precisely two arguments (or none, setting the vectors
to two empty	ones), and they	must be	the same length.

correlation() cor() corr()
Returns a Statistics::Basic::Correlation object.  Arguments to
"correlation()" or "cor()"/"corr()" must be array ref or vector
objects.  There must	be precisely two arguments (or none, setting
the vectors to two empty ones), and they must be the	same length.

leastsquarefit()	LSF() lsf()
Returns a Statistics::Basic::LeastSquareFit object.	Arguments to
"leastsquarefit()" or "lsf()"/"LSF()" must be array ref or vector
objects.  There must	be precisely two arguments (or none, setting
the vectors to two empty ones), and they must be the	same length.

computed()
Returns a Statistics::Basic::ComputedVector object.	Argument must
be a	blessed	vector object.	See the	section	on "COMPUTED VECTORS"

handle_missing_values() handle_missing()
Returns two Statistics::Basic::ComputedVector objects.  Arguments
to this function should be two vector arguments.  See the section
on "MISSING VALUES" for further information on this function.

COMPUTED VECTORS
Sometimes it will be handy to have a vector computed from another (or
at least	that updates based on the first).  Consider the	case of
outliers:

my @a = ( (1,2,3) x 7, 15 );
my @b = ( (1,2,3) x 7 );

my \$v1 = vector(@a);
my \$v2 = vector(@b);
my \$v3 = computed(\$v1);
\$v3->set_filter(sub {
my \$m	= mean(\$v1);
my \$s	= stddev(\$v1);

grep { abs(\$_-\$m) <= \$s } @_;
});

This filter sets	\$v3 to always be equal to \$v1 such that	all the
elements	that differ from the mean by more than a standard deviation
are removed.  As	such, "\$v2" eq "\$v3" since 15 is clearly an outlier by
inspection.

print "\$v1\n";
print "\$v3\n";

... prints:

[1, 2, 3, 1,	2, 3, 1, 2, 3, 1, 2, 3,	1, 2, 3, 1, 2, 3, 1, 2,	3, 15]
[1, 2, 3, 1,	2, 3, 1, 2, 3, 1, 2, 3,	1, 2, 3, 1, 2, 3, 1, 2,	3]

MISSING	VALUES
Something I get asked about quite a lot is, "can	S::B handle missing
values?"	 The answer used to be,	"that really depends on	your data set,
use grep," but I	recently decided (5/29/09) that	it was time to just go

Strictly	speaking, the feature was already there.  You simply need to
the test	example.

This is what people usually mean	when they ask if S::B can "handle"
missing data:

my \$v1 = vector(1,2,3,undef,4);
my \$v2 = vector(1,2,3,4, undef);
my \$v3 = computed(\$v1);
my \$v4 = computed(\$v2);

\$v3->set_filter(sub {
my @v = \$v2->query;
map {\$_[\$_]} grep { defined \$v[\$_] and defined \$_[\$_] } 0 .. \$#_;
});

\$v4->set_filter(sub {
my @v = \$v1->query;
map {\$_[\$_]} grep { defined \$v[\$_] and defined \$_[\$_] } 0 .. \$#_;
});

print "\$v1 \$v2\n"; #	prints:	[1, 2, 3, _, 4]	[1, 2, 3, 4, _]
print "\$v3 \$v4\n"; #	prints:	[1, 2, 3] [1, 2, 3]

But I've	made it	even simpler.  Since this is such a common request, I
have provided a helper function to build	the filters automatically:

my \$v1 = vector(1,2,3,undef,4);
my \$v2 = vector(1,2,3,4, undef);

my (\$f1, \$f2) = handle_missing_values(\$v1, \$v2);

print "\$f1 \$f2\n"; #	prints:	[1, 2, 3] [1, 2, 3]

Note that in practice, you would	still manipulate (insert, and shift)
\$v1 and \$v2, not	the computed vectors.  But for correlations and	the
like, you would use \$f1 and \$f2.

\$v1->insert(5);
\$v2->insert(6);

my \$correlation = correlation(\$f1, \$f2);

You can still insert on \$f1 and \$f2, but	it updates the input vector
rather than the computed	one (which is just a filter handler).

REUSE DETAILS
Most of the objects have	a variety of query functions that allow	you to
extract the objects used	within.	 Although, the objects are smart
enough to prevent needless duplication.	That is, the following would
test would pass:

use Statistics::Basic qw(:all);

my \$v1 = vector(1,2,3,4,5);
my \$v2 = vector(\$v1);
my \$sd = stddev( \$v1	);
my \$v3 = \$sd->query_vector;
my \$m1 = mean( \$v1 );
my \$m2 = \$sd->query_mean;
my \$m3 = Statistics::Basic::Mean->new( \$v1 );
my \$v4 = \$m3->query_vector;

use Test; plan tests	=> 5;

# this is t/54_* in the distribution

Also, note that the mean	is only	calculated once	even though we've
calculated a variance and a standard deviation above.

Suppose you'd like a copy of the	Statistics::Basic::Variance object
that the	Statistics::Basic::StdDev object is using.  All	of the objects
within should be	accessible with	query functions	as follows.

QUERY FUNCTIONS
query()
This	method exists in all of	the objects.
Statistics::Basic::LeastSquareFit is	the only one that returns two
values (alpha and beta) as a	list.  Statistics::Basic::Vector
returns either the list of elements in the vector, or reference to
that	array (depending on the	context).  All of the other "query()"
methods return a single number, the number the module purports to
calculate.

query_mean()
Returns the Statistics::Basic::Mean object used by
Statistics::Basic::Variance and Statistics::Basic::StdDev.

query_mean1()
Returns the first Statistics::Basic::Mean object used by
Statistics::Basic::Covariance, Statistics::Basic::Correlation and
Statistics::Basic::LeastSquareFit.

query_mean2()
Returns the second Statistics::Basic::Mean object used by
Statistics::Basic::Covariance, and Statistics::Basic::Correlation.

query_covariance()
Returns the Statistics::Basic::Covariance object used by
Statistics::Basic::Correlation and
Statistics::Basic::LeastSquareFit.

query_variance()
Returns the Statistics::Basic::Variance object used by
Statistics::Basic::StdDev.

query_variance1()
Returns the first Statistics::Basic::Variance object	used by
Statistics::Basic::LeastSquareFit.

query_vector()
Returns the Statistics::Basic::Vector object	used by	any of the
single vector modules.

query_vector1()
Returns the first Statistics::Basic::Vector object used by any of
the two vector modules.

query_vector2()
Returns the second Statistics::Basic::Vector	object used by any of
the two vector modules.

is_multimodal()
Statistics::Basic::Mode objects sometimes return
Statistics::Basic::Vector objects instead of	numbers.  When
"is_multimodal()" is	true, the mode is a vector, not	a scalar.

y_given_x()
Statistics::Basic::LeastSquareFit is	meant for finding a line of
best	fit.  This function can	be used	to find	the "y"	for a given
"x" based on	the calculated \$beta (slope) and \$alpha	(y-offset).

x_given_y()
Statistics::Basic::LeastSquareFit is	meant for finding a line of
best	fit.  This function can	be used	to find	the "x"	for a given
"y" based on	the calculated \$beta (slope) and \$alpha	(y-offset).

This	function can produce divide-by-zero errors since it must
divide by the slope to find the "x" value.  (The slope should
rarely be zero though, that's a vertical line and would represent
very	odd data points.)

INSERT and SET FUNCTIONS
These objects are all intended to be useful while processing long
columns of data,	like data you'd	find in	a database.

insert()
Vectors try to stay the same	size when they accept new elements,
FIFO	style.

my \$v1 =	vector(1,2,3); # a 3 touple
\$v1->insert(4); # still a 3 touple

print "\$v1\n"; #	prints:	[2, 3, 4]

\$v1->insert(7); # still a 3 touple
print "\$v1\n"; #	prints:	[3, 4, 7]

All of the other Statistics::Basic modules have this	function too.
The modules that track two vectors will need	two arguments to
insert though.

my \$mean	= mean([1,2,3]);
\$mean->insert(4);

print "mean: \$mean\n"; #	prints 3 ... (2+3+4)/3

my \$correlation = correlation(\$mean->query_vector,
\$mean->query_vector->copy);

print "correlation: \$correlation\n"; # 1

\$correlation->insert(3,4);
print "correlation: \$correlation\n"; # 0.5

Also, note that the underlying vectors keep track of	recalculating
automatically.

my \$v = vector(1,2,3);
my \$m = mean(\$v);
my \$s = stddev(\$v);

The mean has	not been calculated yet.

print "\$s; \$m\n"; # 0.82; 2

The mean has	been calculated	once (even though the
Statistics::Basic::StdDev uses it).

\$v->insert(4); print "\$s; \$m\n";	0.82; 3
\$m->insert(5); print "\$s; \$m\n";	0.82; 4
\$s->insert(6); print "\$s; \$m\n";	0.82; 5

The mean has	been calculated	thrice more and	only thrice more.

append()	ginsert()
You can grow	the vectors instead of sliding them (FIFO). For	this,
use "append()" (or "ginsert()", same	thing).

my \$v = vector(1,2,3);
my \$m = mean(\$v);
my \$s = stddev(\$v);

\$v->append(4); print "\$s; \$m\n";	1.12; 2.5
\$m->append(5); print "\$s; \$m\n";	1.41; 3
\$s->append(6); print "\$s; \$m\n";	1.71; 1.71

print "\$v\n"; # [1, 2, 3, 4, 5, 6]
print "\$s\n"; # 1.71

Of course, with a correlation, or a covariance, it'd	look more like
this:

my \$c = correlation([1,2,3], [3,4,5]);
\$c->append(7,7);

print "c=\$c\n"; # c=0.98

set_vector()
This	allows you to set the vector to	a known	state.	It takes
either array	ref or vector objects.

my \$v1 =	vector(1,2,3);
my \$v2 =	\$v1->copy;
\$v2->set_vector([4,5,6]);

my \$m = mean();

\$m->set_vector([1,2,3]);
\$m->set_vector(\$v2);

my \$c = correlation();

\$c->set_vector(\$v1,\$v2);
\$c->set_vector([1,2,3], [4,5,6]);

set_size()
This	sets the size of the vector.  When the vector is made bigger,
the vector is filled	to the new length with leading zeros (i.e.,
they	are the	first to be kicked out after new "insert()"s.

my \$v = vector(1,2,3);
\$v->set_size(7);

print "\$v\n"; # [0, 0, 0, 0, 1, 2, 3]

my \$m = mean();
\$m->set_size(7);

print "", \$m->query_vector, "\n";
# [0, 0, 0, 0, 0, 0, 0]

my \$c = correlation(,);
\$c->set_size(7);

print "", \$c->query_vector1, "\n";
print "", \$c->query_vector2, "\n";
# [0, 0, 0, 0, 0, 0, 3]
# [0, 0, 0, 0, 0, 0, 3]

OPTIONS
Each of the following options can be specified on package import	like
this.

When specified on import, each option has certain defaults.

Additionally, with the exception	of "ignore_env", they can all be
accessed	via package variables of the same name in all upper case.
Example:

# code code code

\$Statistics::Basic::UNBIAS =	0; # turn UNBIAS off

# code code code

\$Statistics::Basic::UNBIAS =	1; # turn it back on

# code code code

{
local \$Statistics::Basic::DEBUG_STATS_B = 1; # debug, this block	only
}

Special caveat: "toler" can in fact be changed via the package var
(e.g., "\$Statistics::Basic::TOLER=0.0001").  But, for speed reasons, it
must be defined before any other	packages are imported or it will not
actually	do anything when changed.

unbias
This	module uses the	sum(X -	mean(X))/N definition of variance.

If you wish to use the unbiased, sum(X-mean(X)/(N-1)	definition,
then	set the	\$Statistics::Basic::UNBIAS true	(possibly with "use
Statistics::Basic qw(unbias)").

This	can be changed at any time with	the package variable or	at
compile time.

This	feature	was requested by "Robert McGehee
<xxxxxxxx@wso.williams.edu>".

[NOTE 2008-11-06:
<http://cpanratings.perl.org/dist/Statistics-Basic>,	this can also
be called "population (n)" vs "sample (n-1)"	and is indeed fully

ipres
"ipres" defaults to 2.  It is passed	to Number::Format as the
second argument to format_number() during string interpolation

toler
When	set, \$Statistics::Basic::TOLER (which is not enabled by
default), instructs the stats objects to test true when within some
tolerable range, pretty much	like this:

sub is_equal {
return abs(\$_-\$_)<\$Statistics::Basic::TOLER
if defined(\$Statistics::Basic::TOLER)

return \$_	== \$_
}

For performance reasons, this must be defined before	the import of
any other Statistics::Basic modules or the modules will fail	to

\$Statistics::Basic::TOLER totally disabled:

use Statistics::Basic qw(:all toler);

\$Statistics::Basic::TOLER disabled, but changeable:

use Statistics::Basic qw(:all toler=0);

\$Statistics::Basic::TOLER = 0.000_001;

You can change the tolerance	at runtime, but	it must	be set (or
unset) at compile time before the packages load.

nofill
Normally when you set the size of a vector it automatically fills
with	zeros on the first-out side of the vector.  You	can disable
the autofilling with	this option.  It can be	changed	at any time.

debug
Enable debugging with "use Statistics::Basic	qw(debug)" or disable
a specific level (including 0 to disable) with "use
Statistics::Basic qw(debug=2)".

This	is also	accessible at runtime using
\$Statistics::Basic::DEBUG_STATS_B and can be	switched on and	off at
any time.

ignore_env
Normally the	defaults for these options can be changed in the
environment of the program.	Example:

UNBIAS=1	perl ./myprog.pl

This	does the same thing as "\$Statistics::Basic::UNBIAS=1" or "use
Statistics::Basic qw(unbias)" unless	you disable the	%ENV checking
with	this option.

use Statistics::Basic qw(ignore_env);

ENVIRONMENT VARIABLES
You can change the defaults (assuming ignore_env	is not used) from your
bash prompt.  Example:

DEBUG_STATS_B=1 perl	./myprog.pl

\$ENV{DEBUG_STATS_B}
Sets	the default value of "debug".

\$ENV{UNBIAS}
Sets	the default value of "unbias".

\$ENV{NOFILL}
Sets	the default value of "nofill".

\$ENV{IPRES}
Sets	the default value of "ipres".

\$ENV{TOLER}
Sets	the default value of "toler".

All of the objects are true in numeric context.	All of the objects
print useful strings when evaluated as a	string.	 Most of the objects
evaluate	usefully as numbers, although Statistics::Basic::Vector
objects,	Statistics::Basic::ComputedVector objects, and
Statistics::Basic::LeastSquareFit objects do not	-- they	instead	raise
an error.

Author's note on Statistics::Descriptive
I've been asked a couple	times now why I	don't link to
to packages there that I	think are related or that I actually used in
the package construction.  I've never personally	used Descriptive, but
it surely seems to do quite a lot more.	In a sense, this package
really doesn't do statistics, not like a	scientist would	think about it
anyway.	So I always figured people could find their own	way to
Descriptive anyway.

The one thing this package does do, that	I don't	think Descriptive does
(correct	me if I'm wrong) is time difference computations.  If there
are say,	200 things in the mean object, then after inserting (using
this package) there'll still be 200 things, allowing the	computation of
a moving	average, moving	stddev,	moving correlation, etc.  You might
argue that this is rarely needed, but it	is really the only time	I need
to compute these	things.

while(	\$data =	\$fetch_sth->fetchrow_arrayref )	{
\$mean->insert(\$data);
\$moving_avg_sth->execute(0	+ \$mean);
}

Since I opened the topic	I'd also like to mention that I	find this
package easier to use.  That is a matter	of taste and since I wrote
this, you might say I'm a little	biased.	 Your mileage may vary.

AUTHOR
Paul Miller "<jettero@cpan.org>"

I am using this software	in my own projects...  If you find bugs,
it handy	at all.	 Half the fun of releasing this	stuff is knowing that
people use it.

Statistics::Basic::ComputedVector, Statistics::Basic::_OneVectorBase,
Statistics::Basic::Mean,	Statistics::Basic::Median,
Statistics::Basic::Mode,	Statistics::Basic::Variance,
Statistics::Basic::StdDev, Statistics::Basic::_TwoVectorBase,
Statistics::Basic::Correlation, Statistics::Basic::Covariance,
Statistics::Basic::LeastSquareFit

perl v5.24.1			  2012-01-23		  Statistics::Basic(3)
```

NAME | SYNOPSIS | SHORTCUTS | COMPUTED VECTORS | MISSING VALUES | REUSE DETAILS | QUERY FUNCTIONS | INSERT and SET FUNCTIONS | OPTIONS | ENVIRONMENT VARIABLES | OVERLOADS | Author's note on Statistics::Descriptive | AUTHOR | COPYRIGHT | SEE ALSO

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