implied_vol::special_function

Trait SpecialFn

Source 
pub trait SpecialFn {
    // Provided methods
    fn erf(x: f64) -> f64 { ... }
    fn erfc(x: f64) -> f64 { ... }
    fn erfcx(x: f64) -> f64 { ... }
    fn erfinv(x: f64) -> f64 { ... }
    fn inverse_norm_cdf(x: f64) -> f64 { ... }
    fn norm_pdf(x: f64) -> f64 { ... }
}
Expand description

The SpecialFn trait provides a collection of special mathematical functions that are commonly used in statistics, probability, and scientific computations. These methods are implemented to calculate specific special functions such as the error function (erf) and its complement, inverse error functions, the normal probability density function, and the inverse cumulative distribution function for a standard normal distribution.

§Required Methods

§erf

Computes the error function erf(x). The error function gives the probability of a random variable from a normal distribution falling within a certain range of standard deviations.

§erfc

Computes the complementary error function erfc(x) which is defined as 1 - erf(x). It is often used to simplify formulas for survival or tail probability distributions.

§erfcx

Computes the scaled complementary error function erfcx(x) defined as exp(x^2) * erfc(x). It is often used to avoid numerical instability in calculations involving the complementary error function.

§erfinv

Computes the inverse error function erfinv(x). This function determines the value of the argument that produces the given value for the error function, i.e., it satisfies erf(erfinv(x)) = x.

§inverse_norm_cdf

Computes the inverse of the cumulative distribution function (quantile function) for a standard normal distribution. That is, for a given probability x in the range [0, 1], it returns the value z such that the probability of a standard normal random variable N(0, 1) being less than z equals x.

§norm_pdf

Computes the probability density function of the standard normal distribution N(0, 1). This function evaluates the PDF at a given input x.

§7. norm_cdf

Computes the Cumulative Distribution Function (CDF) of the standard normal distribution at a given x.

  • This method is only available if the "normal-distribution" feature is enabled.
  • The CDF quantifies the probability that a normally distributed random variable will be less than or equal to x.
  • This function delegates to normal_distribution::norm_cdf.

§Feature Flags

  • The method norm_cdf is available only when the "normal-distribution" feature flag is enabled.

Provided Methods§

Source

fn erf(x: f64) -> f64

Source

fn erfc(x: f64) -> f64

Source

fn erfcx(x: f64) -> f64

Source

fn erfinv(x: f64) -> f64

Source

fn inverse_norm_cdf(x: f64) -> f64

Source

fn norm_pdf(x: f64) -> f64

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§