1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
|
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2002 - INRIA - Carlos Klimann
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function t=trimmean(x,discard,orien, verbose)
//
//A trimmed mean is calculated by discarding a certain
//percentage of the lowest and the highest scores and then
//computing the mean of the remaining scores. For
//example, a mean trimmed 50% is computed by discarding
//the lower and higher 25% of the scores and taking the
//mean of the remaining scores.
//
//The median is the mean trimmed 100% and the arithmetic
//mean is the mean trimmed 0%.
//
//A trimmed mean is obviously less susceptible to the
//effects of extreme scores than is the arithmetic mean.
//It is therefore less susceptible to sampling fluctuation
//than the mean for extremely skewed distributions. It is
//less efficient (The efficiency of a statistic is the
//degree to which the statistic is stable from sample to
//sample. That is, the less subject to sampling
//fluctuation a statistic is, the more efficient it
//is. The efficiency of statistics is measured relative to
//the efficiency of other statistics and is therefore
//often called the relative efficiency. If statistic A has
//a smaller standard error than statistic B, then
//statistic A is more efficient than statistic B. The
//relative efficiency of two statistics may depend on the
//distribution involved. For instance, the mean is more
//efficient than the median for normal distributions but
//not for some extremely skewed distributions. The
//efficiency of a statistic can also be thought of as the
//precision of the estimate: The more efficient the
//statistic, the more precise the statistic is as an
//estimator of the parameter.[from
//http://davidmlane.com/hyperstat/A12977.html]) than the
//mean for normal distributions.
//
//Trimmed means are often used in Olympic scoring to
//minimize the effects of extreme ratings possibly caused
//by biased judges. [from
//http://davidmlane.com/hyperstat/A11971.html]
//
//
//For a vector or matrix x, t=trimmean(x,discard) returns
//in scalar t the mean of all the entries of x, after
//discarding discard/2 highest values and discard/2 lowest
//values.
//
//t=trimmean(x,discard,'r') (or, equivalently,
//t=trimmean(x,discard,1)) returns in each entry of the
//row vector t the trimmed mean of each column of x.
//
//t=trimmean(x,discard,'c') (or, equivalently,
//t=trimmean(x,discard,2)) returns in each entry of the
//column vector t the trimmed mean of each row of x.
//
//References: Luis Angel Garcia-Escudero and Alfonso
//Gordaliza, Robustness Properties of Means and Trimmed
//Means, JASA, Volume 94, Number 447, Sept 1999, pp956-969
//
//
// modified by Bruno Pincon 2006-08-12 (to fix bug 2083)
[lhs,rhs]=argn()
if rhs < 1 | rhs > 4 then
error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"trimmean",1,4))
end
if exists("discard","local")==0 then
discard = 50.
else
if type(discard)~=1 | ~isreal(discard) | length(discard) ~=1 | discard > 100 | discard < 0 then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Real number between %d to %d expected.\n"),"trimmean",2,0,100))
end
end
if exists("orien","local")==0 then
orien = "all"
end
if exists("verbose","local")==0 then
verbose=0;
end
// Compute sizx
if (orien=="r" | orien==1) then
sizx=size(x,"r")
elseif (orien=="c" | orien==2) then
sizx=size(x,"c")
elseif (orien == "all") then
sizx = length(x)
else
error(msprintf(gettext("Wrong value for input argument orien: %s.\n"),string(orien)))
end
if sizx==0 then
if (verbose==1) then
printf(gettext("Size of x is zero : returning NaN.\n"));
end
t=%nan
return
end
nomdis = floor(sizx*discard/200)
k1 = 1 + nomdis
k2 = sizx - nomdis
if k2 < k1 then
[k1,k2] = (k2,k1)
end
nb = k2-k1+1
if (verbose==1) then
printf(gettext("discard=%s\n"),string(discard));
printf(gettext("orien=%s\n"),string(orien));
printf(gettext("Size of x:%i\n"),sizx);
printf(gettext("Keeping %i values from %i to %i in sorted order\n"),nb,k1,k2);
end
if orien == "all" then
x = gsort(x)
t = sum(x(k1:k2)) / nb
elseif (orien=="r" | orien==1) then
x = gsort(x,"r")
t = sum(x(k1:k2,:),"r") / nb
elseif (orien=="c" | orien==2) then
x = gsort(x,"c")
t = sum(x(:,k1:k2),"c") / nb
else
error(msprintf(gettext("Unexpected value of orien : %s\n"),string(orien)))
end
endfunction
|
