Surjunctive group

From formulasearchengine
Jump to navigation Jump to search

The Cornish–Fisher expansion is a mathematical expression used to approximate the quantiles of a random variable based only on its first few cumulants.[1][2][3]

Definition

Let x be a random variable with a density function f(x) with a mean of zero and a variance of 1. Let β1 be the skewness of this distribution and let β2 be its kurtosis. Let z be a normally distributed random variable and let zα be the value of z at the αth percentile.

As an illustration of this last definition when α = 0.95, zα = 1.96

Then

where ωα is the corresponding value for f(x).

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  1. Cornish EA and Fisher RA (1938) Moments and cumulants in the specification of distributions. Revue de l’Institut Internat. de Statistique. 5: 307–322
  2. Fisher RA and Cornish EA (1960) The percentile points of distributions having known cumulants. Technometrics 2: 209–225
  3. Abramowitz M and Stegun I (1965) Handbook of mathematical functions, with formulas, graphs and mathematical tables. Dover Publications, New York