line |
stmt |
bran |
cond |
sub |
pod |
time |
code |
1
|
|
|
|
|
|
|
package Statistics::TheilSenEstimator; |
2
|
|
|
|
|
|
|
|
3
|
1
|
|
|
1
|
|
31390
|
use 5.006; |
|
1
|
|
|
|
|
4
|
|
|
1
|
|
|
|
|
52
|
|
4
|
1
|
|
|
1
|
|
5
|
use strict; |
|
1
|
|
|
|
|
2
|
|
|
1
|
|
|
|
|
32
|
|
5
|
1
|
|
|
1
|
|
6
|
use Carp; |
|
1
|
|
|
|
|
12
|
|
|
1
|
|
|
|
|
81
|
|
6
|
1
|
|
|
1
|
|
5
|
use warnings FATAL => 'all'; |
|
1
|
|
|
|
|
1
|
|
|
1
|
|
|
|
|
63
|
|
7
|
|
|
|
|
|
|
require Exporter; |
8
|
|
|
|
|
|
|
|
9
|
|
|
|
|
|
|
our @ISA = qw/Exporter/; |
10
|
1
|
|
|
1
|
|
920
|
use Statistics::QuickMedian qw/qmedian/; |
|
1
|
|
|
|
|
455
|
|
|
1
|
|
|
|
|
1296
|
|
11
|
|
|
|
|
|
|
|
12
|
|
|
|
|
|
|
our @EXPORT_OK = qw/theilsen/; |
13
|
|
|
|
|
|
|
|
14
|
|
|
|
|
|
|
=head1 NAME |
15
|
|
|
|
|
|
|
|
16
|
|
|
|
|
|
|
Statistics::TheilSen - Perl implementation of Theil Sen Estimator |
17
|
|
|
|
|
|
|
|
18
|
|
|
|
|
|
|
=head1 VERSION |
19
|
|
|
|
|
|
|
|
20
|
|
|
|
|
|
|
Version 0.06 |
21
|
|
|
|
|
|
|
|
22
|
|
|
|
|
|
|
=cut |
23
|
|
|
|
|
|
|
|
24
|
|
|
|
|
|
|
our $VERSION = '0.06'; |
25
|
|
|
|
|
|
|
|
26
|
|
|
|
|
|
|
|
27
|
|
|
|
|
|
|
=head1 SYNOPSIS |
28
|
|
|
|
|
|
|
|
29
|
|
|
|
|
|
|
This is a perl implementation of the Theil Sen Estimator, which is a method of |
30
|
|
|
|
|
|
|
linear regression that uses medians. All of the gradients of the lines between |
31
|
|
|
|
|
|
|
all points are calculated, and hte median is the one reported. Sounds trivial. |
32
|
|
|
|
|
|
|
If you have 1000s of points, then you have millions of lines, and sort-based |
33
|
|
|
|
|
|
|
median methods can take ages, so Statistics::TheilSen uses the partition-based |
34
|
|
|
|
|
|
|
Statistics::QuickMedian. |
35
|
|
|
|
|
|
|
|
36
|
|
|
|
|
|
|
# OOP... |
37
|
|
|
|
|
|
|
|
38
|
|
|
|
|
|
|
use Statistics::TheilSenEstimator; |
39
|
|
|
|
|
|
|
|
40
|
|
|
|
|
|
|
my $tse = Statistics::TheilSenEstimator->new(\$y_values, \$x_values); |
41
|
|
|
|
|
|
|
# which is really a shortcut for: |
42
|
|
|
|
|
|
|
my $tse = Statistics::TheilSenEstimator->new(); |
43
|
|
|
|
|
|
|
$tse->addData(\@y_values, \@x_values); # listrefs of numeric scalars |
44
|
|
|
|
|
|
|
|
45
|
|
|
|
|
|
|
my $status_line = $tse->run(); # might tell if you had bad values, etc |
46
|
|
|
|
|
|
|
print "y = ", $tse->m(), "x + ", $tse->c(); # y = mx + c |
47
|
|
|
|
|
|
|
|
48
|
|
|
|
|
|
|
# or procedural... |
49
|
|
|
|
|
|
|
|
50
|
|
|
|
|
|
|
use Statistics::TheilSenEstimator qw/theilsen/; |
51
|
|
|
|
|
|
|
|
52
|
|
|
|
|
|
|
my ($m,$c) = theilsen(\@y_values, \@x_values); |
53
|
|
|
|
|
|
|
|
54
|
|
|
|
|
|
|
=head1 EXPORT/SUBROUTINES |
55
|
|
|
|
|
|
|
|
56
|
|
|
|
|
|
|
=head2 theilsen |
57
|
|
|
|
|
|
|
|
58
|
|
|
|
|
|
|
Accepts two list refs, the lists should be the same length. They represent y and x series |
59
|
|
|
|
|
|
|
which will be the subject of the regression. Returns a list of two |
60
|
|
|
|
|
|
|
|
61
|
|
|
|
|
|
|
use Statistics::TheilSenEstimator qw/theilsen/; |
62
|
|
|
|
|
|
|
|
63
|
|
|
|
|
|
|
my ($m,$b) = theilsen(\$y_values, \$x_values); |
64
|
|
|
|
|
|
|
|
65
|
|
|
|
|
|
|
=cut |
66
|
|
|
|
|
|
|
|
67
|
|
|
|
|
|
|
sub theilsen { |
68
|
0
|
|
|
0
|
1
|
|
my ($y,$x) = @_; |
69
|
0
|
|
|
|
|
|
my $n = @$y; |
70
|
0
|
0
|
|
|
|
|
carp "y and x series are different lengths" |
71
|
|
|
|
|
|
|
unless $n == @$x; |
72
|
|
|
|
|
|
|
# all the gradients! |
73
|
0
|
|
|
|
|
|
my @M = (); |
74
|
|
|
|
|
|
|
# each item from start to penultimate |
75
|
0
|
|
|
|
|
|
my ($x1,$x2,$y1,$y2); |
76
|
0
|
|
|
|
|
|
foreach my $i(0 .. $n-2){ |
77
|
0
|
|
|
|
|
|
$y1 = $y->[$i]; |
78
|
0
|
|
|
|
|
|
$x1 = $x->[$i]; |
79
|
0
|
0
|
0
|
|
|
|
next unless defined $y1 && $y1 =~ /\d/ && defined $x1 && $x1 =~ /\d/; |
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
80
|
|
|
|
|
|
|
# each item from next to last |
81
|
0
|
|
|
|
|
|
foreach my $j($i+1 .. $n-1){ |
82
|
0
|
|
|
|
|
|
$y2 = $y->[$j]; |
83
|
0
|
0
|
0
|
|
|
|
next unless defined $y2 && $y2 =~ /\d/; |
84
|
|
|
|
|
|
|
# short cut for zero (even if dx is zero ;-) |
85
|
0
|
0
|
|
|
|
|
if($y2 == $y1){ |
86
|
0
|
|
|
|
|
|
push @M, 0; |
87
|
0
|
|
|
|
|
|
next; |
88
|
|
|
|
|
|
|
} |
89
|
0
|
|
|
|
|
|
$x2 = $x->[$j]; |
90
|
0
|
0
|
0
|
|
|
|
next unless defined $x2 && $x2 =~ /\d/; |
91
|
|
|
|
|
|
|
# skip any divisions by zero! (don't add to the list, if it's infinite then it's both pos and neg anyway!) |
92
|
0
|
0
|
|
|
|
|
next if $x2 == $x1; |
93
|
|
|
|
|
|
|
# otherwise, calculate the gradient and push it... |
94
|
0
|
|
|
|
|
|
push @M, ($y2-$y1)/($x2-$x1); |
95
|
|
|
|
|
|
|
} |
96
|
|
|
|
|
|
|
} |
97
|
|
|
|
|
|
|
# now we have @M, so what's the median? |
98
|
0
|
|
|
|
|
|
my $m = qmedian(\@M); # warning... this modifies the order of M! |
99
|
|
|
|
|
|
|
|
100
|
|
|
|
|
|
|
# y-intercept b to be the median of the values yi - mxi |
101
|
0
|
|
|
|
|
|
my @C = (); |
102
|
0
|
|
|
|
|
|
foreach my $i(0 .. $n-1){ |
103
|
0
|
|
|
|
|
|
$y1 = $y->[$i]; |
104
|
0
|
|
|
|
|
|
$x1 = $x->[$i]; |
105
|
0
|
0
|
0
|
|
|
|
next unless defined $y1 && $y1 =~ /\d/ && defined $x1 && $x1 =~ /\d/; |
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
106
|
0
|
|
|
|
|
|
push @C, $y1 - $m * $x1; |
107
|
|
|
|
|
|
|
} |
108
|
|
|
|
|
|
|
# now we have @C, so what's the median? |
109
|
0
|
|
|
|
|
|
my $c = qmedian(\@C); # warning... this modifies the order of C! |
110
|
0
|
|
|
|
|
|
return ($m,$c); |
111
|
|
|
|
|
|
|
} |
112
|
|
|
|
|
|
|
|
113
|
|
|
|
|
|
|
=head1 METHODS |
114
|
|
|
|
|
|
|
|
115
|
|
|
|
|
|
|
=head2 new |
116
|
|
|
|
|
|
|
|
117
|
|
|
|
|
|
|
use Statistics::TheilSenEstimator; |
118
|
|
|
|
|
|
|
my $tse = Statistics::TheilSenEstimator->new(); |
119
|
|
|
|
|
|
|
#or |
120
|
|
|
|
|
|
|
my $tse = Statistics::TheilSenEstimator->new(\@y_values, \@x_values); |
121
|
|
|
|
|
|
|
|
122
|
|
|
|
|
|
|
returns a new Statistics::TheilSenEstimator estimator object with the optional data added. |
123
|
|
|
|
|
|
|
|
124
|
|
|
|
|
|
|
=cut |
125
|
|
|
|
|
|
|
|
126
|
|
|
|
|
|
|
sub new { |
127
|
0
|
|
|
0
|
1
|
|
my $p = shift; |
128
|
0
|
|
0
|
|
|
|
my $c = ref $p || $p; |
129
|
0
|
|
|
|
|
|
my $o = { |
130
|
|
|
|
|
|
|
Y=>[], # we store y series here |
131
|
|
|
|
|
|
|
X=>[], # and x here |
132
|
|
|
|
|
|
|
runSinceAddData=>0, # check whether a run is needed |
133
|
|
|
|
|
|
|
m=>'', |
134
|
|
|
|
|
|
|
c=>'', |
135
|
|
|
|
|
|
|
}; |
136
|
0
|
|
|
|
|
|
bless $o, $c; |
137
|
0
|
0
|
|
|
|
|
if(@_==2){ |
|
|
0
|
|
|
|
|
|
138
|
0
|
|
|
|
|
|
$o->addData(@_); |
139
|
|
|
|
|
|
|
} |
140
|
|
|
|
|
|
|
elsif(@_){ |
141
|
0
|
|
|
|
|
|
croak "wrong number of args to Statistics::TheilSen->new, should be 0 or 2."; |
142
|
|
|
|
|
|
|
} |
143
|
0
|
|
|
|
|
|
return $o; |
144
|
|
|
|
|
|
|
} |
145
|
|
|
|
|
|
|
|
146
|
|
|
|
|
|
|
=head2 addData |
147
|
|
|
|
|
|
|
|
148
|
|
|
|
|
|
|
$tse->addData(\@y_values, \@x_values); |
149
|
|
|
|
|
|
|
|
150
|
|
|
|
|
|
|
Adds data to the y and x series. Data series should be the same length. |
151
|
|
|
|
|
|
|
|
152
|
|
|
|
|
|
|
=cut |
153
|
|
|
|
|
|
|
|
154
|
|
|
|
|
|
|
sub addData { |
155
|
0
|
|
|
0
|
1
|
|
my $o = shift; |
156
|
0
|
0
|
|
|
|
|
croak "wrong number of args to Statistics::TheilSen->new, should be 0 or 2." |
157
|
|
|
|
|
|
|
unless @_ == 2; |
158
|
0
|
|
|
|
|
|
my ($Y,$X) = @_; |
159
|
0
|
0
|
|
|
|
|
croak "Y and X are not equal lengths" |
160
|
|
|
|
|
|
|
unless @$Y == @$X; |
161
|
0
|
|
|
|
|
|
push @{$o->{Y}}, @$Y; |
|
0
|
|
|
|
|
|
|
162
|
0
|
|
|
|
|
|
push @{$o->{X}}, @$X; |
|
0
|
|
|
|
|
|
|
163
|
0
|
|
|
|
|
|
$o->{runSinceAddData} = 0; |
164
|
|
|
|
|
|
|
} |
165
|
|
|
|
|
|
|
|
166
|
|
|
|
|
|
|
=head2 run |
167
|
|
|
|
|
|
|
|
168
|
|
|
|
|
|
|
my $status_line = $tse->run(); |
169
|
|
|
|
|
|
|
|
170
|
|
|
|
|
|
|
Runs the estimator on the data currently in the object. Returns any messages |
171
|
|
|
|
|
|
|
about whether errors or weird things were found in the data. Sets m and c in |
172
|
|
|
|
|
|
|
the object |
173
|
|
|
|
|
|
|
|
174
|
|
|
|
|
|
|
=cut |
175
|
|
|
|
|
|
|
|
176
|
|
|
|
|
|
|
sub run { |
177
|
0
|
|
|
0
|
1
|
|
my $o = shift; |
178
|
|
|
|
|
|
|
# fatal: |
179
|
0
|
|
|
|
|
|
my $n = @{$o->{Y}}; |
|
0
|
|
|
|
|
|
|
180
|
0
|
|
|
|
|
|
return "Y and X are different lengths (fatal)" |
181
|
0
|
0
|
|
|
|
|
if $n != @{$o->{X}}; |
182
|
|
|
|
|
|
|
|
183
|
|
|
|
|
|
|
# "warnings" about data |
184
|
0
|
|
|
|
|
|
my $message; |
185
|
|
|
|
|
|
|
# count up how many of x2-x1 == 0... |
186
|
0
|
|
|
|
|
|
my %X = (); |
187
|
0
|
|
|
|
|
|
my $divZeroCounts = 0; |
188
|
0
|
|
|
|
|
|
foreach (@{$o->{X}}){ |
|
0
|
|
|
|
|
|
|
189
|
0
|
0
|
|
|
|
|
if(exists $X{$_}){ |
190
|
0
|
|
|
|
|
|
$X{$_}++; |
191
|
0
|
|
|
|
|
|
$divZeroCounts += $X{$_}; |
192
|
|
|
|
|
|
|
} |
193
|
|
|
|
|
|
|
else { |
194
|
0
|
|
|
|
|
|
$X{$_} = 0; |
195
|
|
|
|
|
|
|
} |
196
|
|
|
|
|
|
|
} |
197
|
0
|
|
|
|
|
|
undef %X; |
198
|
0
|
0
|
|
|
|
|
if($divZeroCounts){ |
199
|
0
|
|
|
|
|
|
$message .= "Denominator (x2-x1) is zero in $divZeroCounts cases. "; |
200
|
|
|
|
|
|
|
} |
201
|
|
|
|
|
|
|
# check missing values, etc. |
202
|
0
|
|
|
|
|
|
my ($y,$x); |
203
|
0
|
|
|
|
|
|
my $missing = 0; |
204
|
0
|
|
|
|
|
|
foreach my $i(0..$n-1){ |
205
|
0
|
|
|
|
|
|
($y,$x) = ($o->{Y}->[$i],$o->{X}->[$i]); |
206
|
0
|
0
|
0
|
|
|
|
if(! defined $y || $y !~ /\d/ || $y != $y+0 |
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
207
|
|
|
|
|
|
|
|| ! defined $x || $x !~ /\d/ || $x != $x+0){ |
208
|
|
|
|
|
|
|
# looks like x or y is NaN |
209
|
0
|
|
|
|
|
|
$missing ++; |
210
|
|
|
|
|
|
|
} |
211
|
|
|
|
|
|
|
} |
212
|
0
|
0
|
|
|
|
|
if($missing){ |
213
|
0
|
|
|
|
|
|
$message .= "Missing values on $missing rows. "; |
214
|
|
|
|
|
|
|
} |
215
|
|
|
|
|
|
|
# end of checks |
216
|
0
|
|
|
|
|
|
($o->{m}, $o->{c}) |
217
|
|
|
|
|
|
|
= theilsen( |
218
|
|
|
|
|
|
|
$o->{Y}, |
219
|
|
|
|
|
|
|
$o->{X}, |
220
|
|
|
|
|
|
|
); |
221
|
0
|
|
|
|
|
|
$o->{runSinceAddData} = 1; |
222
|
0
|
|
|
|
|
|
return $message; |
223
|
|
|
|
|
|
|
} |
224
|
|
|
|
|
|
|
|
225
|
|
|
|
|
|
|
=head2 m |
226
|
|
|
|
|
|
|
|
227
|
|
|
|
|
|
|
my $gradient = $tse->m(); |
228
|
|
|
|
|
|
|
|
229
|
|
|
|
|
|
|
Returns "m", the gradient of the model generated by run(). If run() was not |
230
|
|
|
|
|
|
|
called since addData(), then run() will be called here! |
231
|
|
|
|
|
|
|
|
232
|
|
|
|
|
|
|
=cut |
233
|
|
|
|
|
|
|
|
234
|
|
|
|
|
|
|
sub m { |
235
|
0
|
|
|
0
|
1
|
|
my $o = shift; |
236
|
0
|
0
|
|
|
|
|
$o->{runSinceAddData} || $o->run(); |
237
|
0
|
|
|
|
|
|
return $o->{m}; |
238
|
|
|
|
|
|
|
} |
239
|
|
|
|
|
|
|
|
240
|
|
|
|
|
|
|
=head2 c |
241
|
|
|
|
|
|
|
|
242
|
|
|
|
|
|
|
my $intersect = $tse->c(); |
243
|
|
|
|
|
|
|
|
244
|
|
|
|
|
|
|
Returns "c", the intersect of the model generated by run(). If run() was not |
245
|
|
|
|
|
|
|
called since addData(), then run() will be called here! |
246
|
|
|
|
|
|
|
|
247
|
|
|
|
|
|
|
=cut |
248
|
|
|
|
|
|
|
|
249
|
|
|
|
|
|
|
sub c { |
250
|
0
|
|
|
0
|
1
|
|
my $o = shift; |
251
|
0
|
0
|
|
|
|
|
$o->{runSinceAddData} || $o->run(); |
252
|
0
|
|
|
|
|
|
return $o->{c}; |
253
|
|
|
|
|
|
|
} |
254
|
|
|
|
|
|
|
|
255
|
|
|
|
|
|
|
=head1 AUTHOR |
256
|
|
|
|
|
|
|
|
257
|
|
|
|
|
|
|
Jimi Wills, C<< >> |
258
|
|
|
|
|
|
|
|
259
|
|
|
|
|
|
|
=head1 BUGS |
260
|
|
|
|
|
|
|
|
261
|
|
|
|
|
|
|
Please report any bugs or feature requests to C, or through |
262
|
|
|
|
|
|
|
the web interface at L. I will be notified, and then you'll |
263
|
|
|
|
|
|
|
automatically be notified of progress on your bug as I make changes. |
264
|
|
|
|
|
|
|
|
265
|
|
|
|
|
|
|
|
266
|
|
|
|
|
|
|
|
267
|
|
|
|
|
|
|
|
268
|
|
|
|
|
|
|
=head1 SUPPORT |
269
|
|
|
|
|
|
|
|
270
|
|
|
|
|
|
|
You can find documentation for this module with the perldoc command. |
271
|
|
|
|
|
|
|
|
272
|
|
|
|
|
|
|
perldoc Statistics::TheilSenEstimator |
273
|
|
|
|
|
|
|
|
274
|
|
|
|
|
|
|
|
275
|
|
|
|
|
|
|
You can also look for information at: |
276
|
|
|
|
|
|
|
|
277
|
|
|
|
|
|
|
=over 4 |
278
|
|
|
|
|
|
|
|
279
|
|
|
|
|
|
|
=item * RT: CPAN's request tracker (report bugs here) |
280
|
|
|
|
|
|
|
|
281
|
|
|
|
|
|
|
L |
282
|
|
|
|
|
|
|
|
283
|
|
|
|
|
|
|
=item * AnnoCPAN: Annotated CPAN documentation |
284
|
|
|
|
|
|
|
|
285
|
|
|
|
|
|
|
L |
286
|
|
|
|
|
|
|
|
287
|
|
|
|
|
|
|
=item * CPAN Ratings |
288
|
|
|
|
|
|
|
|
289
|
|
|
|
|
|
|
L |
290
|
|
|
|
|
|
|
|
291
|
|
|
|
|
|
|
=item * Search CPAN |
292
|
|
|
|
|
|
|
|
293
|
|
|
|
|
|
|
L |
294
|
|
|
|
|
|
|
|
295
|
|
|
|
|
|
|
=back |
296
|
|
|
|
|
|
|
|
297
|
|
|
|
|
|
|
|
298
|
|
|
|
|
|
|
=head1 ACKNOWLEDGEMENTS |
299
|
|
|
|
|
|
|
|
300
|
|
|
|
|
|
|
http://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator |
301
|
|
|
|
|
|
|
|
302
|
|
|
|
|
|
|
=head1 LICENSE AND COPYRIGHT |
303
|
|
|
|
|
|
|
|
304
|
|
|
|
|
|
|
Copyright 2013 Jimi Wills. |
305
|
|
|
|
|
|
|
|
306
|
|
|
|
|
|
|
This program is free software; you can redistribute it and/or modify it |
307
|
|
|
|
|
|
|
under the terms of the the Artistic License (2.0). You may obtain a |
308
|
|
|
|
|
|
|
copy of the full license at: |
309
|
|
|
|
|
|
|
|
310
|
|
|
|
|
|
|
L |
311
|
|
|
|
|
|
|
|
312
|
|
|
|
|
|
|
Any use, modification, and distribution of the Standard or Modified |
313
|
|
|
|
|
|
|
Versions is governed by this Artistic License. By using, modifying or |
314
|
|
|
|
|
|
|
distributing the Package, you accept this license. Do not use, modify, |
315
|
|
|
|
|
|
|
or distribute the Package, if you do not accept this license. |
316
|
|
|
|
|
|
|
|
317
|
|
|
|
|
|
|
If your Modified Version has been derived from a Modified Version made |
318
|
|
|
|
|
|
|
by someone other than you, you are nevertheless required to ensure that |
319
|
|
|
|
|
|
|
your Modified Version complies with the requirements of this license. |
320
|
|
|
|
|
|
|
|
321
|
|
|
|
|
|
|
This license does not grant you the right to use any trademark, service |
322
|
|
|
|
|
|
|
mark, tradename, or logo of the Copyright Holder. |
323
|
|
|
|
|
|
|
|
324
|
|
|
|
|
|
|
This license includes the non-exclusive, worldwide, free-of-charge |
325
|
|
|
|
|
|
|
patent license to make, have made, use, offer to sell, sell, import and |
326
|
|
|
|
|
|
|
otherwise transfer the Package with respect to any patent claims |
327
|
|
|
|
|
|
|
licensable by the Copyright Holder that are necessarily infringed by the |
328
|
|
|
|
|
|
|
Package. If you institute patent litigation (including a cross-claim or |
329
|
|
|
|
|
|
|
counterclaim) against any party alleging that the Package constitutes |
330
|
|
|
|
|
|
|
direct or contributory patent infringement, then this Artistic License |
331
|
|
|
|
|
|
|
to you shall terminate on the date that such litigation is filed. |
332
|
|
|
|
|
|
|
|
333
|
|
|
|
|
|
|
Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT HOLDER |
334
|
|
|
|
|
|
|
AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES. |
335
|
|
|
|
|
|
|
THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR |
336
|
|
|
|
|
|
|
PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT PERMITTED BY |
337
|
|
|
|
|
|
|
YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT HOLDER OR |
338
|
|
|
|
|
|
|
CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, OR |
339
|
|
|
|
|
|
|
CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE OF THE PACKAGE, |
340
|
|
|
|
|
|
|
EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
341
|
|
|
|
|
|
|
|
342
|
|
|
|
|
|
|
|
343
|
|
|
|
|
|
|
=cut |
344
|
|
|
|
|
|
|
|
345
|
|
|
|
|
|
|
1; # End of Statistics::TheilSen |