I played around to understand nature of experimental Distribution and used the nice workflow in JMP Pro 15.0 at Win10 for it (continuous fit --> fit all). JMP showed SHASH Distribution as best fit, where I found mixed normal to fit better. I was able to reconstruct the Problem with a modelled Distribution, see script below. Perhaps negative AIC is the Problem? In the Manual (chapter 3 Basic Analysis, Distributions, p91) I found also that the weighted AIC for the best Distribution is most near to 1. It is the case for SHASH, but it visually and really is wrong, I think. Any Suggestion what the Problem is? Names Default To Here( 1 );
// Compose a distribution with 70 rows random normal, and 30 rows fixed values
Vec = J( 1, 70, Random Normal( 70, 25 ) ) || J( 1, 30, 100 );
// this distribution 70/10 would let JMP take the right guess, but with too small difference in AIC?
// Vec = J( 1, 70, Random Normal( 70, 25 ) ) || J( 1, 10, 100 );
// cut off values larger than 100
Vec[Loc( Vec > 100 )] = 100;
// Put it into table
dty = New Table( "yield_distribution", New Column( "yield", set values( Vec ) ) );
dty << Add Properties to Table(
{New Script(
"Distributions_SHASHvsNormal",
Distribution(
Continuous Distribution( Column( :yield ), CDF Plot( 1 ), Fit Normal 2 Mixture, Fit SHASH ),
SendToReport(
Dispatch( {"yield"}, "Quantiles", OutlineBox, {Close( 1 )} ),
Dispatch( {"yield"}, "Summary Statistics", OutlineBox, {Close( 1 )} ),
Dispatch( {"yield"}, "Fitted Normal 2 Mixture Distribution", OutlineBox, {Close( 1 )} ),
Dispatch(
{"yield", "CDF Plot"},
"Distrib CDF",
FrameBox,
{DispatchSeg(
TopSeg( 2 ),
{Set Script(
Pen Size( 1 );
Pen Color( -2600622 );
Y Function( SHASH Distribution( X, 1.13512094644709, 0.0115544235279409, 100, 9.38305371818249e-80 ), X );
)}
)}
)
)
)
)}
);
dty << run script( "Distributions_SHASHvsNormal" );
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