How can we determine the local maxima in a multi-peaked distribution?

[#1]

We'd like to be able to determine the maximum values of multi-peaked distribution, such as the one below, with some algorithm or utility.

Any ideas how that can be done?

[#2 · Accepted solution]

If you get the number of peaks by inspection, you could try something like this:

NamesDefaultToHere(1);

// Make some random data (with known parameters)

d1 = J(40, 1, RandomNormal(0, 1));

d2 = J(60, 1, RandomNormal(4, 2));

d3 = J(30, 1, RandomNormal(-6, 1));

// Make a table

dt = AsTable(VConcat(d1, d2, d3));

dt << setName("A Mixture of Samples from Three Gaussians");

Column(dt, "Col1") << setName("Y");

// Do a 'Normal Mixtures' analysis

dt << Distribution(

Continuous Distribution(

Column( :Y ),

Vertical( 0 ),

Fit Distribution( Normal Mixtures( Clusters( 3 ) ) )

),

Histograms Only,

SendToReport(

Dispatch(

{"Y"},

"Distrib Histogram",

FrameBox,

{Frame Size( 600, 267 ), DispatchSeg( Hist Seg( 1 ), Bin Span( 2, 0 ) )}

)

)

);