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Ingy döt Net 2026-04-30 12:34:36 -04:00
parent 4bb20c9b71
commit cbaf4c4b64
12390 changed files with 318560 additions and 27248 deletions
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Task/Statistics-Normal-distribution/PHP/statistics-normal-distribution.php Normal file
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<?php
// Statistics/Normal distribution
normal_stats(100);
echo PHP_EOL;
normal_stats(1000);
echo PHP_EOL;
normal_stats(10000);
echo PHP_EOL;
// Generates normally distributed random numbers with $mean 0 and standard deviation 1
function random_normal() {
return cos(2.0 * M_PI * mt_rand() / mt_getrandmax()) *
sqrt(-2.0 * log(mt_rand() / mt_getrandmax()));
}
function normal_stats ($sample_size) {
if ($sample_size < 1) return;
srand((double)microtime() * 1000000);
$r = array_fill(0, $sample_size, 0);
$h = array_fill(0, 12, 0);
$sum = 0.0;
$h_sum = 0;
// Generate '$sample_size' normally distributed random numbers with $mean 0.5
// and standard deviation 0.25
// calculate their $sum
// and in which box they will fall when drawing the histogram
for ($i = 0; $i < $sample_size; $i++) {
$r[$i] = .5 + random_normal() / 4.0;
$sum += $r[$i];
if ($r[$i] < 0.0)
$h[0]++;
else if ($r[$i] >= 1.0)
$h[11]++;
else
$h[ceil($r[$i] * 10)]++;
}
foreach ($h as $h_item)
$h_sum += $h_item;
// adjust one of the $h values if necessary to ensure $h_sum = $sample_size
$adj = $sample_size - $h_sum;
if ($adj != 0) {
for ($i = 0; $i <= 11; $i++) {
$h[$i] += $adj;
if ($h[$i] >= 0) break;
$h[$i] -= $adj;
}
}
$mean = $sum / $sample_size;
$sum = 0.0;
// Now calculate their standard deviation
foreach ($r as $r_item)
$sum += pow($r_item - $mean, 2);
$sd = sqrt($sum / $sample_size);
// Draw a histogram of the data with interval 0.1
// If sample size > 300 then normalize histogram to 300
$scale = 1.0;
if ($sample_size > 300)
$scale = 300.0 / $sample_size;
echo 'Sample size '.$sample_size.PHP_EOL;
echo ' Mean '.
str_pad(number_format($mean, 6, '.', ''), 8, ' ', STR_PAD_LEFT).
' SD '.
str_pad(number_format($sd, 6, '.', ''), 8, ' ', STR_PAD_LEFT).PHP_EOL;
$i = -1;
foreach ($h as $h_item) {
if ($i == -1)
echo '< 0.00 : ';
else if ($i == 10)
echo '>=1.00 : ';
else
echo ' '.
str_pad(number_format($i / 10.0, 2, '.', ''), 4, ' ', STR_PAD_LEFT).
' : ';
echo str_pad($h_item, 5, ' ', STR_PAD_LEFT).' '.
str_repeat('*', round($h_item * $scale)).PHP_EOL;
$i++;
}
}
?>