Density trace (boxcar weight function)                          [STB-16: snp6]
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         ^boxdetr2^ varname width dtrace midpt

Description
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^boxdetra^ calculates the density trace of "varname" using the boxcar weight 
function described in Chambers et. al. (1983).  "width" is a constant that
specifies the width of the density window around each point.  "dtrace" is 
a new variable that contains the density trace on output.  "midpt" is a new
variable that contains the midpoints of the 50 bins within which the 
density is calculated.  The data set is assumed to be sorted in the order 
of "varname".

This procedure can be regarded as a descriptive smoother of histograms.
Indeed this simple density estimator is like a histogram using bins of the
specified width but no fixed origin; the bin's windows run along the 
series with each observation at its midpoint allowing overlap.
The "smoothness" of the result can be regulated by changing the width of
the interval. Wide intervals produce smooth results; narrow intervals
result in noiser density values.

WARNING: Even though ^boxdetr2^ considers only 50 equally spaced bins, 
the computing time required is proportional to the number of observations. 
Please be patient.

Example
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  . ^boxdetr2 ozone 75 dtrace midpt^

After some time (depending on the number of observations) the results are
placed in the new variable ^dtrace^. 

  . ^list midpt dtrace^ in 1/50

lists the values of the data variable and the density trace estimation 
results.

  . ^graph dtrace midpt if _n<51^, xlab ylab c(l) s(p)

displays a graph of the density trace.


References
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   Chambers, J.M., W.S. Cleveland, B. Kleiner and P.A. Tukey (1983)
        Graphical Methods for Data Analysis. Wadsworth & Brooks/Cole
        Chap. 2: 9-46.
   Fox, J. (1990) Describing univariate distributions. In (Fox, J. &
        J.S. Long, Eds.) "Modern Methods of Data Analysis". Sage
        Chap. 2: 58-125.


Authors
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Isaias H. Salgado-Ugarte, Makoto Shimizu and Toru Taniuchi,
University of Tokyo, Faculty of Agriculture,
Dept. of Fisheries (Fax 81-3-3812-0529)

Also see
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    STB: snp6 (STB-16)
On-line: ^help^ for ^boxdetra^, ^cosdetra^, ^kernsim^, ^kernepa^, ^kerngaus^, 
         ^adgakern^, ^adgaker2^