SHRIMP: Function fdNmad

SQUID 2.50 Function: fdNmad

This subroutine evaluates the double-precision value fdNmad (median absolute deviation) corresponding to an input vector v comprising double-precision numbers.

Usage

fdNmad( v )

Mandatory variables

v: Vector containing double-precision values.

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Definition of variables

Values of type Integer
i, N, Nn

Values of type Double
med, medyr2, fdNmad

Arrays of type Double
v, yr2

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The function utilises the Excel function UBound (http://www.excelfunctions.net/vba-ubound-function.html) to determine the length of the input vector:

N = UBound( v ) --like length(v)  
med = Median( v )

Nn = Max( 3, N ) --minimum value of 3
ReDim yr2[1 to N] --apparently not zero-addressed 

For i = 1 to N  
  yr2[i] = ( v[i] - med )^2  
Next i

medyr2 = Median( yr2 )    

fdNmad = 1.4826 * ( 1 + 5 / (Nn - 2) ) * Sqrt( medyr2 )

End Function

The magic number 1.4826 is hard-coded (by Ludwig and by most other users of MAD-related functions: this value ensures that "± MAD" encompasses 50% (i.e. between 1/4 and 3/4) of the normal cumulative distribution function (e.g. https://en.wikipedia.org/wiki/Median_absolute_deviation).