1
$\begingroup$

I was reading Kline’s (2011) textbook on structural equation modeling when I found something extremely interesting: Kline explained that, under a frequentist perspective, probability is based on the expected relative frequency over a large number of trials.  In other words, there isn't a probability associated with whether or not a particular guess is correct.

I'm just a bit confused then on the purpose and interpretation of the negative binomial distribution.  If, given a frequentist perspective, probability can't be associated with singular events, what does the negative binomial distribution mean? Doesn't it describe the the trial on which the rth success occurs in repeated independent Bernoulli trials?

$\endgroup$
0

1 Answer 1

Reset to default
1
$\begingroup$

Say you have a set of repeated Bernoulli trials until you get to the $r$th success. Think of that set of Bernoulli trials as one negative binomial experiment. The frequentist interpretation says that if you run that experiment over and over, as the number of experiments gets larger and larger, the distribution of the number of Bernoulli trials required for $r$ successes converges to the negative binomial distribution.

$\endgroup$
2
  • $\begingroup$ oh my goodness, what a beautiful, short, and clear answer :) thank you so much! $\endgroup$
    – JerBear
    Commented Dec 30, 2020 at 21:02
  • $\begingroup$ You're very welcome! $\endgroup$
    – Amaan M
    Commented Dec 30, 2020 at 21:36

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .