Errorfunction (FSharp.Stats)

Errorfunction Module

Namespace: FSharp.Stats.SpecialFunctions
Assembly: FSharp.Stats.dll

Error function (erf) and related functions. the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: erf (z) = 2/√π * \int e^(-t²) dt from 0 to z This integral is a special (non-elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of x, the error function has the following interpretation: for a random variable Y that is normally distributed with mean 0 and standard deviation 1/√2 , erf x is the probability that Y falls in the range [−x, x].

Functions and values

Function or value	Description
`Erf x` Full Usage: `Erf x` Parameters: x : `float` - Returns: `float`	Computes the error function. Note that this implementation has only been verified to have a relative error of around 1e-5. x : `float` Returns: `float` Example
`Erfc x` Full Usage: `Erfc x` Parameters: x : `float` - Returns: `float`	Computes the complement of the error function. Note that this implementation has only been verified to have a relative error of around 1e-4. x : `float` Returns: `float` Example
`_erfcx x` Full Usage: `_erfcx x` Parameters: x : `float` - Input to compute exp(x*2) erfc(x) Returns: `float`	Scaled complementary error function, exp(x*2) erfc(x). The caller is responsible to handle edge cases such as nan, infinity, and -infinity in the input x : `float` Input to compute exp(x*2) erfc(x) Returns: `float`
`erfcx x` Full Usage: `erfcx x` Parameters: x : `float` - Input to compute exp(x*2) erfc(x) Returns: `float`	Scaled complementary error function, exp(x*2) erfc(x). Edge cases in the input (nan, infinity, and -infinity) are catched and handled. This might be slower than the unchecked version `_erfcx` but does not require input sanitation to get expected results for these cases. x : `float` Input to compute exp(x*2) erfc(x) Returns: `float`
`inverf x` Full Usage: `inverf x` Parameters: x : `float` - Returns: `float`	inverse of error function. uses newton refinement; from https://libit.sourceforge.net/ accuracy to the fifth digit x : `float` Returns: `float` Example
`inverfc x` Full Usage: `inverfc x` Parameters: x : `float` - Returns: `float`	inverse of complementary error function accuracy to the fifth digit x : `float` Returns: `float` Example

Errorfunction Module

Functions and values

Example

Example

Example

Example