#2462 negative_binomial overly restrictive

closed
nobody
None
5
2012-11-02
2012-08-21
No

The negative binomial distribution need not be restricted to integer values of the argument n; cf.
http://en.wikipedia.org/wiki/Negative_binomial_distribution
Indeed, the noninteger case as an overdispersed generalization of the Poisson distribution is important in many fields, including ecology, environmental monitoring, epidemiology, industrial safety, insurance, medicine, microbiology, etc.

Here are function definitions for the general negative binomial pdf and cdf

pdf_negative_binomial2(x,n,p) := pdf_beta(p,n,x+1)*p/(n+x)$ /* negative binomial for real n>0 */

cdf_negative_binomial2(x,n,p) := cdf_beta(p,n,x+1)$ /* negative binomial for real n>0 */

The functions for mean, var, std, skewness, and kurtosis should be fine if you just remove the trap for non-integer n. Assuming that the quantile function numerically inverts the cdf, then it would likely be fine too.

Discussion

  • Jerry W. Lewis

    Jerry W. Lewis - 2012-08-21
    • summary: negative_binomial overly retrictive --> negative_binomial overly restrictive
     
  • Mario Rodriguez Riotorto

    Thanks for bringing this to our attention.

    It's now fixed in git repository. Instead of using pdf_beta, we call beta_incomplete_regularized and the floor function to take into account the discrete nature of the r.v.

    Also, quantile_negative_binomial needed a bug fix.

    --
    Mario

     
  • Raymond Toy

    Raymond Toy - 2012-11-02

    Actually close the bug.

     
  • Raymond Toy

    Raymond Toy - 2012-11-02
    • status: open --> closed
     

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