In probability theory and statistics, the split normal distribution also known as the two-piece normal distribution results from joining at the mode the corresponding halves of two normal distributions with the same mode but different variances. It is claimed by Johnson et al.[1] that this distribution was introduced by Gibbons and Mylroie[2] and by John.[3] But these are two of several independent rediscoveries of the Zweiseitige Gauss'sche Gesetz introduced in the posthumously published Kollektivmasslehre (1897)[4] of Gustav Theodor Fechner (1801-1887), see Wallis (2014).[5] Another rediscovery has appeared more recently in a finance journal.[6]
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Split-normalNotation |
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— mode (location, real) — left-hand-side standard deviation (scale, real) — right-hand-side standard deviation (scale, real) |
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