I'm looking for some information on the "Extreme Value" distribution type, found in the Distribution Platform under Continuous Fit. Specifically, what is the formula for this cumulative distribution? Here's an example:
Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Big Class.jmp");
Distribution(
Continuous Distribution(
Column(:height),
Quantiles(0),
Histogram(0),
Vertical(0),
Outlier Box Plot(0),
Normal Quantile Plot(1),
Fit Distribution(Extreme Value(Spec Limits(LSL(50), USL(70))))
)
);
Here's a pic of the fit in the Distribution report. There are two parameters, lambda and delta.
I checked the "JSL Syntax Reference > JSL Functions > Probability Functions". The closest functions I can see are the "SEV Distribution" and "LEV Distribution", which both also take 2 parameters in addition to the independent variable x.
However, the values I get using either of these functions with the parameters in the Distribution report do not jibe. E.G: at my LSL of 50, the report says 0.9904% of the distrubution is below my lower limit. However:
x = 50; //my LSL
mu = 4.1650529; //taken from report
sigma = 0.0548885; //taken from report
pLEV = LEV Distribution(x, mu, sigma);
pSEV = SEV Distribution(x, mu, sigma);
Show(pLEV, pSEV);
Both functions return a probability of 100%. In fact, they remain 100% unless I lower x to ~4. So clearly either these aren't the right functions or I'm missing something.
Any ideas?