TeXipedia

Finv

Represents the inverse of the cumulative distribution function (CDF) in probability and statistics.

Overview

Essential in statistical analysis and probability theory for finding quantiles and critical values of distributions.

  • Commonly used when working with probability distributions to find specific percentiles
  • Appears frequently in hypothesis testing and confidence interval calculations
  • Important in quantitative finance for calculating Value at Risk (VaR)
  • Used in statistical software documentation and research papers discussing statistical methods

Examples

Inverse Fourier transform of a function f(ω).

Ⅎ[f(ω)]=12π∫−∞∞f(ω)eiωt dω\Finv[f(\omega)] = \frac{1}{2\pi} \int_{-\infty}^{\infty} f(\omega)e^{i\omega t}\,d\omega 
\Finv[f(\omega)] = \frac{1}{2\pi} \int_{-\infty}^{\infty} f(\omega)e^{i\omega t}\,d\omega

Composition of a function with its inverse Fourier transform.

Ⅎ[F(f)]=f\Finv[\mathcal{F}(f)] = f 
\Finv[\mathcal{F}(f)] = f

Signal processing equation showing inverse Fourier transform relationship.

x(t)=Ⅎ[X(ω)]x(t) = \Finv[X(\omega)] 
x(t) = \Finv[X(\omega)]