### Re: Bernoulli and the "critical" and "invcdf" functions

Good afternoon.
I run gretl 1.9.92 64-bit for Windows.
For 0.05 < prob < 0.95
The function
critical(B, prob, 1, p=0.05)
returns the value "1".
As the Help says, the function "returns x such that P(X > x) = p". Since
number of trials is equal to 1, we just have a Bernoulli, with P(X=0) =
1-prob and P(X=1) =prob. So by returning "1" the function asserts that
P(X > 1) = 0.05 > 0
If the function returned "0" it would assert that P(X > 0) = 0.05 < prob
=P(X=1)
I take note of the asymmetry (in the first case, the function "sends
some probability to the right"), -can this be the rule that leads to the
function returning "1"?
Now, the function
invcdf(B, prob, 1, 0.05)
returns "NA"
As the Help says the function "returns x such that P(X ≤ x) = p"
So here a return of "1" would assert P(X =<1) = 0.05 < 1, while a return
of "0" would assert that P(X =<0) =0.05 < 1-Prob.
Here in both cases, returning a number, either 0 or 1, would
"under-signal" the true probability - so maybe this is the reason why
here we get "NA"?
It appears as a choice to prefer making the rejection of a null
hypothesis harder rather than easier... but most probably I am imagining
things.
Can somebody shed some light?
--
--
Alecos Papadopoulos
Athens University of Economics and Business, Greece
Department of Economics
cell:+30-6945-378680
fax: +30-210-8259763
skype:alecos.papadopoulos
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