getMessage(); } if (($value <= 0) || ($stdDev <= 0)) { return Functions::NAN(); } return StandardNormal::cumulative((log($value) - $mean) / $stdDev); } /** * LOGNORM.DIST. * * Returns the lognormal distribution of x, where ln(x) is normally distributed * with parameters mean and standard_dev. * * @param mixed $value Float value for which we want the probability * Or can be an array of values * @param mixed $mean Mean value as a float * Or can be an array of values * @param mixed $stdDev Standard Deviation as a float * Or can be an array of values * @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false) * Or can be an array of values * * @return array|float|string The result, or a string containing an error * If an array of numbers is passed as an argument, then the returned result will also be an array * with the same dimensions */ public static function distribution($value, $mean, $stdDev, $cumulative = false) { if (is_array($value) || is_array($mean) || is_array($stdDev) || is_array($cumulative)) { return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $mean, $stdDev, $cumulative); } try { $value = DistributionValidations::validateFloat($value); $mean = DistributionValidations::validateFloat($mean); $stdDev = DistributionValidations::validateFloat($stdDev); $cumulative = DistributionValidations::validateBool($cumulative); } catch (Exception $e) { return $e->getMessage(); } if (($value <= 0) || ($stdDev <= 0)) { return Functions::NAN(); } if ($cumulative === true) { return StandardNormal::distribution((log($value) - $mean) / $stdDev, true); } return (1 / (sqrt(2 * M_PI) * $stdDev * $value)) * exp(0 - ((log($value) - $mean) ** 2 / (2 * $stdDev ** 2))); } /** * LOGINV. * * Returns the inverse of the lognormal cumulative distribution * * @param mixed $probability Float probability for which we want the value * Or can be an array of values * @param mixed $mean Mean Value as a float * Or can be an array of values * @param mixed $stdDev Standard Deviation as a float * Or can be an array of values * * @return array|float|string The result, or a string containing an error * If an array of numbers is passed as an argument, then the returned result will also be an array * with the same dimensions * * @TODO Try implementing P J Acklam's refinement algorithm for greater * accuracy if I can get my head round the mathematics * (as described at) http://home.online.no/~pjacklam/notes/invnorm/ */ public static function inverse($probability, $mean, $stdDev) { if (is_array($probability) || is_array($mean) || is_array($stdDev)) { return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $mean, $stdDev); } try { $probability = DistributionValidations::validateProbability($probability); $mean = DistributionValidations::validateFloat($mean); $stdDev = DistributionValidations::validateFloat($stdDev); } catch (Exception $e) { return $e->getMessage(); } if ($stdDev <= 0) { return Functions::NAN(); } return exp($mean + $stdDev * StandardNormal::inverse($probability)); } }