| public static checkLimits ( array $limits, array $params ) : boolean | ||
| $limits | array | Boundary limit definitions for each parameter ['var1' => limit, 'var2' => limit, ...] |
| $params | array | Parameters and their value to check against the defined limits ['var1' => value, 'var2' => value, ...] |
| 리턴 | boolean | True if all parameters are within defined limits |
public static function checkLimits(array $limits, array $params)
{
// All parameters should have limit bounds defined
$undefined_limits = array_diff_key($params, $limits);
if (!empty($undefined_limits)) {
throw new Exception\BadParameterException('Parameter without bounds limit defined: ' . print_r($undefined_limits, true));
}
foreach ($params as $variable => $value) {
// Remove the first character: ( or [
$lower_endpoint = substr($limits[$variable], 0, 1);
// Remove the last character: ) or ]
$upper_endpoint = substr($limits[$variable], -1, 1);
// Set the lower and upper limits: #,#
list($lower_limit, $upper_limit) = explode(',', substr($limits[$variable], 1, -1));
// If the lower limit is -∞, we are always in bounds.
if ($lower_limit != "-∞") {
switch ($lower_endpoint) {
case '(':
if ($value <= $lower_limit) {
throw new Exception\OutOfBoundsException("{$variable} must be > {$lower_limit}");
}
break;
case '[':
if ($value < $lower_limit) {
throw new Exception\OutOfBoundsException("{$variable} must be >= {$lower_limit}");
}
break;
default:
throw new Exception\BadDataException("Unknown lower endpoint character: {$lower_limit}");
}
}
// If the upper limit is ∞, we are always in bounds.
if ($upper_limit != "∞") {
switch ($upper_endpoint) {
case ')':
if ($value >= $upper_limit) {
throw new Exception\OutOfBoundsException("{$variable} must be < {$upper_limit}");
}
break;
case ']':
if ($value > $upper_limit) {
throw new Exception\OutOfBoundsException("{$variable} must be <= {$upper_limit}");
}
break;
default:
throw new Exception\BadDataException("Unknown upper endpoint character: {$upper_endpoint}");
}
}
}
return true;
} /**
* Cumulative Poisson Probability (lower culmulative distribution) - CDF
* The probability that the Poisson random variable is greater than some specified lower limit,
* and less than some specified upper limit.
*
* k λˣℯ^⁻λ
* P(k,λ) = ∑ ------
* ₓ₌₀ xᵢ!
*
* @param int $k events in the interval
* @param float $λ average number of successful events per interval
*
* @return float The cumulative Poisson probability
*/
public static function CDF(int $k, float $λ) : float
{
Support::checkLimits(self::LIMITS, ['k' => $k, 'λ' => $λ]);
return array_sum(array_map(function ($k) use($λ) {
return self::PMF($k, $λ);
}, range(0, $k)));
}
