Hello to everyone,
I have a question concerning the derivation of a confidence intervall
estimate. Say we carry out a Bernoulli experiment n times to estimate
the probability p(A)=p of an event A. As a result, this event may occur
k times. Then the (maximum-likelihood) estimate for p reads
p = k/n.
So far everything is clear. In a script of a statistics lecture given by
C.Cenker at the university of Vienna, cf.
http://www.univie.ac.at/spareg/cc/teaching/VO_StatWinf_bsp.html
on p. 82 I found
p_1/2 = 2 m + ( a^2 +- a sqrt( a^2 + 4 m (1-m/n) ) ) / 2 [ n + a^2 ]
as an exact exact estimate for the confidence intervall [p1, p2] for a
given confidence level of 1-alpha, with
a = phi^(-1)(1-alpha/2),
phi denoting the error function. However, the formula was only given as
a remark, as a recipe, without a derivation. Could someone name me a
reference on that issue? Thanks in advance.
Kind regards,
Volker Knecht
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