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# hs2sign

## PURPOSE

Calculates a ratio-significant value of a histogram.

## SYNOPSIS

hs=hs2sign(f,ratio);

## DESCRIPTION

```  HS2SIGN Calculates a ratio-significant value of a histogram.

CALL: cs = hs2sign(f);
CALL: cs = hs2sign(f,ratio);

cs    = a three column matrix with ratio in the first column
the ratio-significant value of  H in the second and
a ratio-quantile in the third column.
f     = a two column matrix containing the histogram.
ratio = a constant (0<ratio<1) defining the significant value,
(optional input, only one significant value is computed).```

## CROSS-REFERENCE INFORMATION

This function calls:
 diff Difference and approximate derivative. error Display message and abort function.
This function is called by:

## SOURCE CODE

```001 function hs=hs2sign(f,ratio);
002 % HS2SIGN Calculates a ratio-significant value of a histogram.
003 %
004 %  CALL: cs = hs2sign(f);
005 %  CALL: cs = hs2sign(f,ratio);
006 %
007 %        cs    = a three column matrix with ratio in the first column
008 %                the ratio-significant value of  H in the second and
009 %                a ratio-quantile in the third column.
010 %        f     = a two column matrix containing the histogram.
011 %        ratio = a constant (0<ratio<1) defining the significant value,
012 %                (optional input, only one significant value is computed).
013
014 [y index]=sort(f(:,1));
015 f=f(index,:);
016 Hs=cumsum(f(:,2));
017
018 if (nargin<2)
019   f=flipud(f);
020   Hs=cumsum(f(:,2));
021   index=find(Hs>0);
022   f=f(index,:);
023   Hs=cumsum(f(:,2));
024   Fs=flipud(cumsum(f(:,2).*f(:,1))./Hs);
025
026   N=length(Hs);
027
028   NN=sum(f(:,2));
029
030   hs=ones(N,3);
031   hs(:,1)=flipud(Hs)./NN;
032   hs(:,2)=Fs;
033   hs(:,3)=flipud(f(:,1));
034 else
035   if ratio <= 0
036     error('ratio  must be >0.')
037     break
038   end
039   if ratio >= 1
040     error('ratio  must be <1.')
041   end
042   hs=min(Hs./sum(f(:,2)),ones(length(Hs),1).*ratio);
043   dhs=abs(diff([0; f(:,1)]'));
044   hs=[ratio dhs*hs/ratio];
045 end
046```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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