Constructor Detail

• Statistics

  public Statistics()

Method Detail

• erf

  public static double erf(double z)

  Calculates an estimate of the upper tail cumulative normal distribution (which is simply the complementary error function with linear scalings of x and y axis). Fractional error in math formula less than 1.2 * 10 ^ -7. although subject to catastrophic cancellation when z in very close to 0 Code from (thanks to Bob Dougherty): w Original algorithm from Section 6.2 of Numerical Recipes

• phi

  public static double phi(double z)

  Calculates phi, which is the area of the Gaussian standard distribution from minus infinity to the query value in units of standard derivation. The formula is: 1 + erf( z / sqrt(2) ) Phi(z) = ---------------------- 2

  Parameters:

  z - The point of interest

  Returns:

  phi

• phi

  public static double phi(double z,
                           double mean,
                           double sd)

  Calculates phi, but with a Gaussian distribution defined by its mean and its standard derivation. This is a quantile. 1 + erf( (z - mean) / (sqrt(2) * stdDev) ) Phi(z,mean,stdDev) = ------------------------------------------ 2 *

  Parameters:

  z - The point of interest

  mean - The mean of the distribution

  sd - The standard derivation of the distribution

  Returns:

  phi

• stdDeviation

  public static double stdDeviation(List<Double> values)

  Calculates the standard deviation of a list of values.

  Parameters:

  values - The list of values.

  Returns:

  The standard deviation.