Re: [Gretl-users] Bernoulli and the "critical" and "invcdf" functions

Am 16.10.2014 um 05:24 schrieb Alecos Papadopoulos: This part of the doc looks wrong for discrete distributions anyway, because in general you will not be able to hit an x/p-combination with equality if the function is not continuous. I would argue that a function named 'critical' is related to hypothesis testing, so let's think about these tests in a discrete framework. The pre-specified significance level alpha is *not* in general equal to the type-I error of the test, because given the discreteness ("lumpiness") of the prob. distribution that equality is not always possible. So instead the standard definition is that "choose a rejection region such that the type-I error is as large as possible but does not exceed alpha". So with Bernoulli if your H0 is P(X=1) = prob, and you pre-specify your alpha, whenever prob > alpha, you must not include the value 1 in your rejection region, because you would violate your significance level. Since in the definition of 'critical' it says X>x, returning the value 1 does the right thing because it is just barely not included in the rejection region. The more exact definition (perhaps also should be in the docs) would probably be something like this: " returns the minimal possible value x such that still P(X > x) <= p holds". Of course, for the standard continuous case this is probably more confusing than helpful. A CDF for discrete variables is not strictly increasing and thus not invertible. This could be the rationale for NA. Perhaps alternative conventions could be used for invcdf(), but you would have to argue that it's useful or necessary. hth, sven