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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
use PhpOffice\PhpSpreadsheet\Calculation\MathTrig\Combinations;
class Binomial
{
use ArrayEnabled;
/**
* BINOMDIST.
*
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
* when trials are independent, and when the probability of success is constant throughout the
* experiment. For example, BINOMDIST can calculate the probability that two of the next three
* babies born are male.
*
* @param mixed $value Integer number of successes in trials
* Or can be an array of values
* @param mixed $trials Integer umber of trials
* Or can be an array of values
* @param mixed $probability Probability of success on each trial as a float
* Or can be an array of values
* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distribution($value, $trials, $probability, $cumulative)
{
if (is_array($value) || is_array($trials) || is_array($probability) || is_array($cumulative)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $trials, $probability, $cumulative);
}
try {
$value = DistributionValidations::validateInt($value);
$trials = DistributionValidations::validateInt($trials);
$probability = DistributionValidations::validateProbability($probability);
$cumulative = DistributionValidations::validateBool($cumulative);
} catch (Exception $e) {
return $e->getMessage();
}
if (($value < 0) || ($value > $trials)) {
return ExcelError::NAN();
}
if ($cumulative) {
return self::calculateCumulativeBinomial($value, $trials, $probability);
}
/** @var float */
$comb = Combinations::withoutRepetition($trials, $value);
return $comb * $probability ** $value
* (1 - $probability) ** ($trials - $value);
}
/**
* BINOM.DIST.RANGE.
*
* Returns returns the Binomial Distribution probability for the number of successes from a specified number
* of trials falling into a specified range.
*
* @param mixed $trials Integer number of trials
* Or can be an array of values
* @param mixed $probability Probability of success on each trial as a float
* Or can be an array of values
* @param mixed $successes The integer number of successes in trials
* Or can be an array of values
* @param mixed $limit Upper limit for successes in trials as null, or an integer
* If null, then this will indicate the same as the number of Successes
* Or can be an array of values
*
* @return array|float|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function range($trials, $probability, $successes, $limit = null)
{
if (is_array($trials) || is_array($probability) || is_array($successes) || is_array($limit)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $trials, $probability, $successes, $limit);
}
$limit = $limit ?? $successes;
try {
$trials = DistributionValidations::validateInt($trials);
$probability = DistributionValidations::validateProbability($probability);
$successes = DistributionValidations::validateInt($successes);
$limit = DistributionValidations::validateInt($limit);
} catch (Exception $e) {
return $e->getMessage();
}
if (($successes < 0) || ($successes > $trials)) {
return ExcelError::NAN();
}
if (($limit < 0) || ($limit > $trials) || $limit < $successes) {
return ExcelError::NAN();
}
$summer = 0;
for ($i = $successes; $i <= $limit; ++$i) {
/** @var float */
$comb = Combinations::withoutRepetition($trials, $i);
$summer += $comb * $probability ** $i
* (1 - $probability) ** ($trials - $i);
}
return $summer;
}
/**
* NEGBINOMDIST.
*
* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that
* there will be number_f failures before the number_s-th success, when the constant
* probability of a success is probability_s. This function is similar to the binomial
* distribution, except that the number of successes is fixed, and the number of trials is
* variable. Like the binomial, trials are assumed to be independent.
*
* @param mixed $failures Number of Failures as an integer
* Or can be an array of values
* @param mixed $successes Threshold number of Successes as an integer
* Or can be an array of values
* @param mixed $probability Probability of success on each trial as a float
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*
* TODO Add support for the cumulative flag not present for NEGBINOMDIST, but introduced for NEGBINOM.DIST
* The cumulative default should be false to reflect the behaviour of NEGBINOMDIST
*/
public static function negative($failures, $successes, $probability)
{
if (is_array($failures) || is_array($successes) || is_array($probability)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $failures, $successes, $probability);
}
try {
$failures = DistributionValidations::validateInt($failures);
$successes = DistributionValidations::validateInt($successes);
$probability = DistributionValidations::validateProbability($probability);
} catch (Exception $e) {
return $e->getMessage();
}
if (($failures < 0) || ($successes < 1)) {
return ExcelError::NAN();
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
if (($failures + $successes - 1) <= 0) {
return ExcelError::NAN();
}
}
/** @var float */
$comb = Combinations::withoutRepetition($failures + $successes - 1, $successes - 1);
return $comb
* ($probability ** $successes) * ((1 - $probability) ** $failures);
}
/**
* BINOM.INV.
*
* Returns the smallest value for which the cumulative binomial distribution is greater
* than or equal to a criterion value
*
* @param mixed $trials number of Bernoulli trials as an integer
* Or can be an array of values
* @param mixed $probability probability of a success on each trial as a float
* Or can be an array of values
* @param mixed $alpha criterion value as a float
* Or can be an array of values
*
* @return array|int|string
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverse($trials, $probability, $alpha)
{
if (is_array($trials) || is_array($probability) || is_array($alpha)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $trials, $probability, $alpha);
}
try {
$trials = DistributionValidations::validateInt($trials);
$probability = DistributionValidations::validateProbability($probability);
$alpha = DistributionValidations::validateFloat($alpha);
} catch (Exception $e) {
return $e->getMessage();
}
if ($trials < 0) {
return ExcelError::NAN();
} elseif (($alpha < 0.0) || ($alpha > 1.0)) {
return ExcelError::NAN();
}
$successes = 0;
while ($successes <= $trials) {
$result = self::calculateCumulativeBinomial($successes, $trials, $probability);
if ($result >= $alpha) {
break;
}
++$successes;
}
return $successes;
}
/**
* @return float|int
*/
private static function calculateCumulativeBinomial(int $value, int $trials, float $probability)
{
$summer = 0;
for ($i = 0; $i <= $value; ++$i) {
/** @var float */
$comb = Combinations::withoutRepetition($trials, $i);
$summer += $comb * $probability ** $i
* (1 - $probability) ** ($trials - $i);
}
return $summer;
}
}
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