Cauchy Distribution



Cauchy Distribution

The distribution function of a random variable X distributed according to the Cauchy distribution is a continuous function, F(x) = P(X < x), given by
F(x) =
[ 1 / π ] ∫-∞x 1 / (1 + t 2) dt = 1 / 2 + (1 / π) tan -1(x) for -∞ < x < ∞

The corresponding probability density function, f(x) = dF(x)/dx, is
f(x) =
[ 1 / π ] [1 / (1 + x 2)] for -∞ < x < ∞

Function List

  • double Cauchy_Distribution( double x )

    This function returns F(x) where F(x) is described above.

  • double Cauchy_Density( double x )

    This function returns f(x) where f(x) is described above.

  • void Cauchy_Distribution_Tables( double start, double delta, int nsteps, double *density, double* distribution_function )

    This function returns f(x) where f(x) is described above in the array density, i.e. density[i] = f(xi) where xi = start + i delta, i = 0,...,nsteps and returns F(x) where F(x) is described above in the array distribution_function, i.e. distribution_function[i] = F(xi) where xi = start + i delta, i = 0,...,nsteps. Note that density must be declared double density[N] where N ≥ nsteps + 1 in the calling routine and similarly the distribution_function must be declared double distribution_function[N] where
    N ≥ nsteps + 1 in the calling routine.

Source Code

C source code is available for these routines: