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3.2.5 Negative Binomial Distribution - 國立臺灣大學

Negative Binomial DistributionIn a sequence of independent Bernoulli(p) trials, let the random variableXdenote the trialat which therthsuccess occurs, whereris a fixed integer. ThenP(X=x|r, p) =(x 1r 1)pr(1 p)x r, x=r, r+ 1, .. ,(1)and we say thatXhas a Negative Binomial (r, p) Negative Binomial Distribution is sometimes defined in terms of the random variableY=number of failures beforerth success. This formulation is statistically equivalent to theone given above in terms ofX=trial at which therth success occurs, sinceY=X r.

The negative binomial distribution is sometimes defined in terms of the random variable Y =number of failures before rth success. This formulation is statistically equivalent to the one given above in terms of X =trial at which the rth success occurs, since Y = X −r. The

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