In terms of the position of the peak, -pkexamine- will only tell you the
observed value of x that has the highest observed value of y.
If you know (or hypothesise) the underlying functional form of the data,
you could find a theoretical peak by using -nl- to fit a non-linear
model to the data, e.g.
. nl (y = x * exp(-(x - {c})/{r})), init(c 0 r 1) nolog
(obs = 68)
Source | SS df MS
-------------+------------------------------ Number of obs =
68
Model | 5571019.21 2 2785509.61 R-squared =
0.9992
Residual | 4437.80091 66 67.2394078 Adj R-squared =
0.9992
-------------+------------------------------ Root MSE =
8.199964
Total | 5575457.01 68 81992.0149 Res. dev. =
477.1073
------------------------------------------------------------------------
------
y | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
/c | .2423345 .0016988 142.65 0.000 .2389427
.2457263
/r | .0226752 .0001888 120.13 0.000 .0222983
.023052
------------------------------------------------------------------------
------
* (SEs, P values, CIs, and correlations are asymptotic approximations)
If this functional form is correct, then the estimate for the peak is at
0.0227 (the value of the parameter r) and we also have a confidence
interval for it.
However, examining the results graphically shows that this functional
form is clearly wrong...
. twoway function y = x * exp(-(x - _b[c:_cons])/_b[r:_cons]), range(x)
///
|| scatter y x ///
, legend(off) xli(`=_b[r:_cons]')
If the points are as dense as in the example you gave, then just looking
at the point with the highest y value is a good bet. If you have bigger
gaps, you may want to think along these lines but remember that a
slightly wrong function could give you a totally wrong result.
Hope this helps
David
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