nbinpdf

Negative binomial probability density function

Syntax

Y = nbinpdf(X,R,P)


Description

Y = nbinpdf(X,R,P) returns the negative binomial pdf at each of the values in X using the corresponding number of successes, R and probability of success in a single trial, P. X, R, and P can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of Y. A scalar input for X, R, or P is expanded to a constant array with the same dimensions as the other inputs. Note that the density function is zero unless the values in X are integers.

The negative binomial pdf is

$$y=f(x|r,p)=\left(\begin{array}{c}r+x-1\\ x\end{array}\right)p^r{q}^x{I}_{(0,1,\mathrm{...})}(x)$$

The simplest motivation for the negative binomial is the case of successive random trials, each having a constant probability P of success. The number of extra trials you must perform in order to observe a given number R of successes has a negative binomial distribution. However, consistent with a more general interpretation of the negative binomial, nbinpdf allows R to be any positive value, including nonintegers. When R is noninteger, the binomial coefficient in the definition of the pdf is replaced by the equivalent expression

$$\frac{\Gamma (r+x)}{\Gamma (r)\Gamma (x+1)}$$

Examples

Compute the Negative Binomial Distribution pdf

Compute the pdf of a negative binomial distribution with parameters R = 3 and p = 0.5.

x = (0:10);
y = nbinpdf(x,3,0.5);

Plot the pdf.

figure;
plot(x,y,'+')
xlim([-0.5,10.5])

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a