Negative Binomial PDF
y = distfun_nbinpdf(x,R,P)
a matrix of doubles, the extra trials for R successes, in the set {0,1,2,3,...}.
a matrix of doubles, the number of successes. R belongs to the set {0,1,2,3,4,.......}
a matrix of doubles, the probability of getting success in a Bernoulli trial. P in [0,1].
a matrix of doubles, the probability density.
Computes the probability distribution function of the Negative Binomial distribution function.
Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.
The function definition is:
Analysis of the random variable.
Consider successive random trials, each having a constant probability P of success. The number of extra trials we perform in order to observe a given number R of successes has a negative binomial distribution.
// Check with x scalar, R scalar, P scalar p = distfun_nbinpdf(5,2,0.2) expected = 0.0786432 // Check with expanded x computed = distfun_nbinpdf([5 7],5,0.5) expected = [0.1230469 0.0805664] // Check with expanded R computed = distfun_nbinpdf(5,[5 7],0.5) expected = [0.1230469 0.1127930] // Check with two arguments expanded computed = distfun_nbinpdf([5 10],[5 7],0.5) expected = [0.1230469 0.0610962] // Check with all the arguments expanded computed = distfun_nbinpdf([5 10],[5 20],[0.5 0.7]) expected = [0.1230469 0.0943745] // Check y = distfun_nbinpdf(x,R,P) with large value of R computed = distfun_nbinpdf(2,1000,0.5) expected = 1.16D-296 // Plot the function scf(); x = 0:60; y1 = distfun_nbinpdf(x,20,0.5); plot(x,y1,"bo-") y2 = distfun_nbinpdf(x,20,0.7); plot(x,y2,"go-") y3 = distfun_nbinpdf(x,40,0.5); plot(x,y3,"ro-") legend(["P=0.5, R=20","P=0.7, R=20","P=0.5, R=40"]); xtitle("Negative Binomial PDF","x","P(X=x)") | ![]() | ![]() |
http://en.wikipedia.org/wiki/Negative_binomial_distribution