Radico-Normal Distribution


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The Radico-normal distribution is a member of the modified normal distributions constructed by Romanowski [1].

It is a special case of the modified normal cumulative density function (CDF) [1]

with a = ½.

Note that when a is infinitely large, the curve is a normal distribution. When a tends to infinity, the curve becomes a normal distribution. When a = 3 the curve is approximately normal. The ratio between the peak of the modified normal curve and the peak of the corresponding normal curve—with equal variance—is 1.16 for the Radico-normal distribution [2].

Properties of the Radico-Normal Distribution

  • Symmetric about 0.
  • Variance: σ2(a + 1)/(a + 2) = σ2(½ + 1)/( ½ + 2) = σ2(1½ )/( 2½).
  • Kurtosis: 3(a + 2)2/{(a + 1)(a + 3)} = 3(½ + 2)2/{(½ + 1)( ½ + 3)} = 3(2½)2/{(1½)( 3½)}  3.57.

See also:

References

[1] M. ROMANOWSKI: Bull. Géodésique 73, 95 (1964).

[2] Johnson, Kotz, and Balakrishnan, (1994), Continuous Univariate Distributions, Volumes I and II, 2nd. Ed., John Wiley and Sons.