WEIGHTED ORDER STATISTIC MEAN

WEIGHTED ORDER STATISTIC MEAN (LET)

Let Subcommand

Compute the weighted order statistic mean of a variable.

The formula for the weighted order statistic mean is

with X_i and W_i denoting the response variable and the weights variable, respectively.

Note that the X_i will be sorted while the W_i will not be sorted before applying this formula. That is, the W_i weight applies to the i-th order statistic, not the i-th response value. This is the main distinction between this command and the WEIGHTED MEAN command.

LET <par> = WEIGHTED ORDER STATISTIC MEAN <y> <w>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
      <w> is the weights varialbe;
      <par> is a parameter where the weighted order statistic mean is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET WOS = WEIGHTED ORDER STATISTIC MEAN Y1 WEIGHT
LET WOS = WEIGHTED ORDER STATISTIC MEAN Y1 SUBSET TAG = 1

None

None

WEIGHTED MEAN	= Compute the weighted mean of a variable.
WEIGHTED SUM	= Compute the weighted sum of a variable.
WEIGHTED STAND DEVIATION	= Compute the weighted standard deviation of a variable.
MEAN	= Compute the mean of a variable.
CONSENSUS MEANS	= Perform a consensus means analysis.

Consensus Means

2012/11

 
let y = data 1 4 9 16 25
let w = data 0 1 1 1 0
.
let b = weighted order statistic mean y w
    

The computed value of the statistic is 9.666667.

let b = weighted order statistic mean y w
.
title case asis
title offset 2
title Bootstrap Plot for Weighted Order Statistic Means
label case ais
y1label Weighted Order Statistic Mean
x1label Bootstrap Sample
.
bootstrap sample 1000
set write decimals 5
bootstrap weighted order statistic mean plot y w
    

 
            Bootstrap Analysis for the WEIGHTED ORDER STATISTICS MEAN
 
Response Variable One: Y
Response Variable Two: W
 
Number of Bootstrap Samples:                       1000
Number of Observations:                               5
Mean of Bootstrap Samples:                     10.55099
Standard Deviation of Bootstrap Samples:        4.92068
Median of Bootstrap Samples:                    9.66666
MAD of Bootstrap Samples:                       3.99999
Minimum of Bootstrap Samples:                   1.00000
Maximum of Bootstrap Samples:                  25.00000
 
 
 
Percent Points of the Bootstrap Samples
-----------------------------------
  Percent Point               Value
-----------------------------------
            0.1    =        1.00000
            0.5    =        1.00000
            1.0    =        2.00000
            2.5    =        2.00000
            5.0    =        3.66666
           10.0    =        4.66666
           20.0    =        5.66666
           50.0    =        9.66666
           80.0    =       15.00000
           90.0    =       16.66666
           95.0    =       19.00000
           97.5    =       22.00000
           99.0    =       22.00000
           99.5    =       25.00000
           99.9    =       25.00000
 
 
            Percentile Confidence Interval for Statistic
 
------------------------------------------
  Confidence          Lower          Upper
 Coefficient          Limit          Limit
------------------------------------------
       50.00        7.00000       13.66666
       75.00        4.66666       16.66666
       90.00        3.66666       19.00000
       95.00        2.00000       22.00000
       99.00        1.00000       25.00000
       99.90        1.00000       25.00000
------------------------------------------