Hello Stefan,

you are extremely helpful! The paper by John D. Cook, together with the provided software implementation should finish the topic, but let's look at the Amalthea system:

<deviation xmi:id="_HdClXAZ5EeSiF4A9B43Urw">
<lowerBound xsi:type="common:LongObject" xmi:id="_HdClXQZ5EeSiF4A9B43Urw" value="220"/>
<upperBound xsi:type="common:LongObject" xmi:id="_HdClXgZ5EeSiF4A9B43Urw" value="1476"/>
<distribution xsi:type="common:WeibullEstimators" xmi:id="_HdClXwZ5EeSiF4A9B43Urw" pRemainPromille="0.005">
<mean xsi:type="common:LongObject" xmi:id="_HdClYAZ5EeSiF4A9B43Urw" value="432"/>
</distribution>
</deviation>

We need values x1, x2, p1, p2 such that:

P(X < x1) = p1,

P(X < x2) = p2.

As you've written, pRemainPromille is a value of the survival function for x=upperBound. I also assume that the probability of x<lowerBound is very low.

So, for example:

x1=220 //lowerBound

p1=0.001 //an arbitrary low probability value

x2=1476 //upperBound

p2=0.995 //1-pRemainPromille

Then:

gamma=(log(-log(1-p2))-log(-log(1-p1)))/(log(x2)-log(x1))=4.5048 //shape parameter

beta=x1/(-log(1-p1))^(1/gamma)=1.0194e+03 //scale parameter

The mean value for this Weibull distribution is about 930, whereas in the quoted Amalthea extract it is equal to 432. To obtain so low value, I'd have to substitute 0.27 for p1, a rather large value as for a lower bound.

Despite this inconsistency (provided that I haven't done any stupid mistake), I'm finding the technique quite useful for my purpose. Thank you once again.

Best regards,

Piotr Dziurzanski