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