Yoshiro Nagao:
You are asking for the mode of x, but the mode is hard to find in your case since x appears to be a continuous variable in your dataset. What is the most common value of a variable if all values are unique? However, you could smooth the distribution of x (using -kdensity-) and the value of x with the highest density would be a good guess of the mode. Bootstrap this if you want to know confidence intervals, standard errors, etc., like the example below. The "modes" in this program might depend on the halfwidth used in smoothing and the number of points on which the kernel density is evaluated (options n and width of -kdensity-). I have just used the defaults and leave it to you to make sure your results are robust for changes in these parameters.
HTH,
Maarten
*---------------------begin example-------------------
clear
input x y
0.001 51.50260873
0.002 97.07276611
0.004 172.6656633
0.01 307.1488228
0.015 351.7068487
0.018 361.1290563
0.02 362.5851013
0.022 361.1579356
0.025 355.0243609
0.026936 349.2274688
0.03015 337.5129189
0.031578 331.7415732
0.034031 321.3389083
0.034865 317.7105064
0.037063 308.0381902
0.037358 306.7342402
0.037467 306.2523588
0.037474 306.2214115
0.038027 303.776684
0.038251 302.7867493
0.038585 301.311442
0.039193 298.6293865
0.039494 297.3038676
0.039935 295.3652685
0.040106 294.6148147
0.040191 294.2420642
0.040219 294.1193181
0.040488 292.9411912
0.040816 291.5075608
0.041131 290.1339949
0.041507 288.4989377
0.041591 288.1343652
0.041876 286.8994377
0.04228 285.1544511
0.04258 283.8631282
0.043052 281.8395817
0.043103 281.6215528
0.043225 281.1004946
0.043279 280.8700899
0.043478 280.0222289
0.043663 279.2357696
0.043929 278.1079959
0.044 277.8075879
0.044154 277.1569019
0.044216 276.8952895
0.044303 276.5285322
0.044435 275.9728462
0.044584 275.3467259
0.044585 275.3425278
0.044728 274.7427697
0.045133 273.0503312
0.045152 272.9711602
0.045487 271.5786566
0.045712 270.6470581
0.046434 267.6780716
0.046449 267.616725
0.047472 263.4661057
0.047808 262.1174236
0.047822 262.0613878
0.048543 259.1929745
0.048582 259.0388008
0.048648 258.7781234
0.048672 258.683404
0.048733 258.4428326
0.048899 257.7894298
0.048979 257.4752003
0.049285 256.2772735
0.049458 255.6028341
end
capture program drop mode
program define mode, rclass
tempvar xx sx mis dmode
quietly {
kdensity x, nograph generate(`xx' `sx')
gen `mis' = missing(`sx')
sort `mis' `sx'
by `mis': gen double `dmode' = `xx'[_N]
return scalar mode = `dmode'
}
end
bootstrap "mode" r(mode), reps(1000)
*---------------------end example--------------------
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
-----Original Message-----
From: [email protected] [mailto:[email protected]]On Behalf Of Yoshiro Nagao
Sent: dinsdag 11 april 2006 10:18
To: [email protected]
Subject: st: finding a peak in an asymmetric curve
Are there any statistical method
to find the value of x for the peak,
and show its "significance"?
*
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