Perl Statistics::Descriptive and a trimmed standard deviation

Question

Statistics::Descriptive 模块提供了 Full 类，可让您计算截尾平均值。有没有办法从中得到修剪的标准偏差？它已经对数据进行排序以获得修剪均值，因此困难的部分已经完成。

Answer 1

如果您的数据全部为正数或全部为负数，那么您可以只保留 2 个 $stat 对象，一个用于普通值，一个用于平方值，并组合 trimmed_mean 结果以生成修剪后的 stddev:

my $stat_x = Statistics::Descriptive::Full->new();
my $stat_xx = Statistics::Descriptive::Full->new();
sub add_x {
  $stat_x->add_data( @_ );
  $stat_xx->add_data( map {$_*$_} @_ );
}
sub trimmed_stddev {
  my $lower = shift;
  my $upper = @_ ? shift : $lower;  

  my $trm_x = $stat_x->trimmed_mean( $lower, $upper );
  my $trm_xx = $stat_xx->trimmed_mean( $lower, $upper );

  my $nn = int( $stat_x->count() * ( 1.0 - $lower - $upper ) );

  return ($nn <= 1 ? 0.0 : sqrt(($trm_xx - $trm_x * $trm_x ) * $nn / ($nn -1)) );
}

# add some data 
add_x( 1, 5, 12, 29, 10, 11, 2 );

print trimmed_stddev(0.0);
print trimmed_stddev(0.05);
print trimmed_stddev(0.2);
# output
#    9.45163125250522
#    9.58570364061576
#    4.44222166638871