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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 distribution function (CDF) [1]

with *a* = ½.

Note that when *a* is infinitely large, the curve is 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: σ
^{2}(*a*+ 1)/(*a*+ 2) = σ^{2}(½ + 1)/( ½ + 2) = σ^{2}(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.

Related distributions:

- Equi-Normal Distribution (
*a*= 1). - Lineo-Normal Distribution (
*a*= 1). - Quadri-Normal Distribution (
*a*= 2).

## 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.