Gamma
extends GammaBase
in package
uses
ArrayEnabled
Table of Contents
Methods
- distribution() : array<string|int, mixed>|float|string
- GAMMADIST.
- gamma() : array<string|int, mixed>|float|string
- GAMMA.
- gammaValue() : float
- incompleteGamma() : float
- inverse() : array<string|int, mixed>|float|string
- GAMMAINV.
- ln() : array<string|int, mixed>|float|string
- GAMMALN.
- logGamma() : float
- logGamma function.
- calculateDistribution() : float
- calculateInverse() : float|string
- evaluateArrayArguments() : array<string|int, mixed>
- Handles array argument processing when the function accepts multiple arguments, and any of them can be an array argument.
- evaluateArrayArgumentsIgnore() : array<string|int, mixed>
- Handles array argument processing when the function accepts multiple arguments, and any of them can be an array argument except for the one specified by ignore.
- evaluateArrayArgumentsSubset() : array<string|int, mixed>
- Handles array argument processing when the function accepts multiple arguments, but only the first few (up to limit) can be an array arguments.
- evaluateArrayArgumentsSubsetFrom() : array<string|int, mixed>
- Handles array argument processing when the function accepts multiple arguments, but only the last few (from start) can be an array arguments.
- evaluateSingleArgumentArray() : array<string|int, mixed>
- Handles array argument processing when the function accepts a single argument that can be an array argument.
- logGamma3() : float
- logGamma4() : float
Methods
distribution()
GAMMADIST.
public
static distribution(mixed $value, mixed $a, mixed $b, mixed $cumulative) : array<string|int, mixed>|float|string
Returns the gamma distribution.
Parameters
- $value : mixed
-
Float Value at which you want to evaluate the distribution Or can be an array of values
- $a : mixed
-
Parameter to the distribution as a float Or can be an array of values
- $b : mixed
-
Parameter to the distribution as a float Or can be an array of values
- $cumulative : mixed
-
Boolean value indicating if we want the cdf (true) or the pdf (false) Or can be an array of values
Return values
array<string|int, mixed>|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
gamma()
GAMMA.
public
static gamma(mixed $value) : array<string|int, mixed>|float|string
Return the gamma function value.
Parameters
- $value : mixed
-
Float value for which we want the probability Or can be an array of values
Return values
array<string|int, mixed>|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
gammaValue()
public
static gammaValue(float $value) : float
Parameters
- $value : float
Return values
floatincompleteGamma()
public
static incompleteGamma(float $a, float $x) : float
Parameters
- $a : float
- $x : float
Return values
floatinverse()
GAMMAINV.
public
static inverse(mixed $probability, mixed $alpha, mixed $beta) : array<string|int, mixed>|float|string
Returns the inverse of the Gamma distribution.
Parameters
- $probability : mixed
-
Float probability at which you want to evaluate the distribution Or can be an array of values
- $alpha : mixed
-
Parameter to the distribution as a float Or can be an array of values
- $beta : mixed
-
Parameter to the distribution as a float Or can be an array of values
Return values
array<string|int, mixed>|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
ln()
GAMMALN.
public
static ln(mixed $value) : array<string|int, mixed>|float|string
Returns the natural logarithm of the gamma function.
Parameters
- $value : mixed
-
Float Value at which you want to evaluate the distribution Or can be an array of values
Return values
array<string|int, mixed>|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
logGamma()
logGamma function.
public
static logGamma(float $x) : float
Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
The natural logarithm of the gamma function.
Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz
Applied Mathematics Division
Argonne National Laboratory
Argonne, IL 60439
References:
- W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.
- K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.
- Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.
From the original documentation:
This routine calculates the LOG(GAMMA) function for a positive real argument X. Computation is based on an algorithm outlined in references 1 and 2. The program uses rational functions that theoretically approximate LOG(GAMMA) to at least 18 significant decimal digits. The approximation for X > 12 is from reference 3, while approximations for X < 12.0 are similar to those in reference 1, but are unpublished. The accuracy achieved depends on the arithmetic system, the compiler, the intrinsic functions, and proper selection of the machine-dependent constants.
Error returns:
The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
The computation is believed to be free of underflow and overflow.
Parameters
- $x : float
Tags
Return values
float —MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
calculateDistribution()
protected
static calculateDistribution(float $value, float $a, float $b, bool $cumulative) : float
Parameters
- $value : float
- $a : float
- $b : float
- $cumulative : bool
Return values
floatcalculateInverse()
protected
static calculateInverse(float $probability, float $alpha, float $beta) : float|string
Parameters
- $probability : float
- $alpha : float
- $beta : float
Return values
float|stringevaluateArrayArguments()
Handles array argument processing when the function accepts multiple arguments, and any of them can be an array argument.
protected
static evaluateArrayArguments(callable $method, mixed ...$arguments) : array<string|int, mixed>
Example use for: ROUND() or DATE().
Parameters
- $method : callable
- $arguments : mixed
Return values
array<string|int, mixed>evaluateArrayArgumentsIgnore()
Handles array argument processing when the function accepts multiple arguments, and any of them can be an array argument except for the one specified by ignore.
protected
static evaluateArrayArgumentsIgnore(callable $method, int $ignore, mixed ...$arguments) : array<string|int, mixed>
Example use for: HLOOKUP() and VLOOKUP(), where argument 1 is a matrix that needs to be treated as a database rather than as an array argument.
Parameters
- $method : callable
- $ignore : int
- $arguments : mixed
Return values
array<string|int, mixed>evaluateArrayArgumentsSubset()
Handles array argument processing when the function accepts multiple arguments, but only the first few (up to limit) can be an array arguments.
protected
static evaluateArrayArgumentsSubset(callable $method, int $limit, mixed ...$arguments) : array<string|int, mixed>
Example use for: NETWORKDAYS() or CONCATENATE(), where the last argument is a matrix (or a series of values) that need to be treated as a such rather than as an array arguments.
Parameters
- $method : callable
- $limit : int
- $arguments : mixed
Return values
array<string|int, mixed>evaluateArrayArgumentsSubsetFrom()
Handles array argument processing when the function accepts multiple arguments, but only the last few (from start) can be an array arguments.
protected
static evaluateArrayArgumentsSubsetFrom(callable $method, int $start, mixed ...$arguments) : array<string|int, mixed>
Example use for: Z.TEST() or INDEX(), where the first argument 1 is a matrix that needs to be treated as a dataset rather than as an array argument.
Parameters
- $method : callable
- $start : int
- $arguments : mixed
Return values
array<string|int, mixed>evaluateSingleArgumentArray()
Handles array argument processing when the function accepts a single argument that can be an array argument.
protected
static evaluateSingleArgumentArray(callable $method, array<string|int, mixed> $values) : array<string|int, mixed>
Example use for: DAYOFMONTH() or FACT().
Parameters
- $method : callable
- $values : array<string|int, mixed>
Return values
array<string|int, mixed>logGamma3()
protected
static logGamma3(float $y) : float
Parameters
- $y : float
Return values
floatlogGamma4()
protected
static logGamma4(float $y) : float
Parameters
- $y : float