function pdf = negative_binomial_pdf ( x, a, b ) %*****************************************************************************80 % %% NEGATIVE_BINOMIAL_PDF evaluates the Negative Binomial PDF. % % Formula: % % PDF(X)(A,B) = C(X-1,A-1) * B^A * ( 1 - B )^(X-A) % % Discussion: % % PDF(X)(A,B) is the probability that the A-th success will % occur on the X-th trial, given that the probability % of a success on a single trial is B. % % The Negative Binomial PDF is also known as the Pascal PDF or % the "Polya" PDF. % % NEGATIVE_BINOMIAL_PDF(X)(1,B) = GEOMETRIC_PDF(X)(B) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 19 September 2004 % % Author: % % John Burkardt % % Parameters: % % Input, integer X, the number of trials. % A <= X. % % Input, integer A, the number of successes required. % 0 <= A <= X, normally. % % Input, real B, the probability of a success on a single trial. % 0.0 < B <= 1.0. % % Output, real PDF, the value of the PDF. % if ( x < a ) pdf = 0.0; else cnk = i4_choose ( x - 1, a - 1 ); pdf = cnk * b ^ a * ( 1.0 - b ) ^ ( x - a ); end return end