use strict;
use warnings;
+sub wilson_interval {
+ my ($x, $n) = @_;
+ my $z = 1.96; # 95% confidence interval
+
+ my $p = $x / $n;
+ my $min = ($p + $z * $z / (2 * $n) - $z * sqrt($p * (1 - $p) / $n + $z * $z / (4 * $n * $n))) / (1 + $z * $z / $n);
+ my $max = ($p + $z * $z / (2 * $n) + $z * sqrt($p * (1 - $p) / $n + $z * $z / (4 * $n * $n))) / (1 + $z * $z / $n);
+
+ $min = 0 if ($min < 0);
+
+ return ($min, $max);
+}
+
my %buckets = ();
while (<>) {
}
for my $n (sort { $a <=> $b } keys %buckets) {
- my $drop_rate = $buckets{$n}->{'num_drops'} / ($n * $buckets{$n}->{'num_bursts'});
- my $drop_event_rate = ($buckets{$n}->{'bursts_with_drops'} // 0) / $buckets{$n}->{'num_bursts'};
- printf "%3d: drop_rate %.5f drop_event_rate %.5f\n",
- $n, $drop_rate, $drop_event_rate;
+ my $num_bursts = $buckets{$n}->{'num_bursts'} // 0;
+ my $num_drops = $buckets{$n}->{'num_drops'} // 0;
+ my $bursts_with_drops = $buckets{$n}->{'bursts_with_drops'} // 0;
+
+ my $drop_rate = $num_drops / ($n * $num_bursts);
+ my $drop_event_rate = $bursts_with_drops / $num_bursts;
+
+ my ($drop_rate_min, $drop_rate_max) = wilson_interval($num_drops, $n * $num_bursts);
+ my ($drop_event_rate_min, $drop_event_rate_max) = wilson_interval($bursts_with_drops, $num_bursts);
+
+ printf "%3d: drop_rate %.5f 95%%ci = [%.5f, %.5f] (%4d/%8d) drop_event_rate %.5f 95%%ci = [%.5f, %.5f] (%3d/%4d)\n",
+ $n,
+ $drop_rate, $drop_rate_min, $drop_rate_max, $num_drops, $n * $num_bursts,
+ $drop_event_rate, $drop_event_rate_min, $drop_event_rate_max, $bursts_with_drops, $num_bursts;
}