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Fitting negative binomial distribution by maximum likelihood 

        nbfit varname [if exp] [in range] [weight] [, log ]


Description 

nbfit fits a negative binomial distribution to a single variable by the method
of maximum likelihood. Frequency weights may be used to fit variables given in
frequency distribution form.

The distribution is here parameterised by m (estimated by the mean) and k:

             Gamma(k + x)               k               x
    pr(x) =  ------------  (k / (k + m))   (m / (k + m))
             Gamma(k) x!

             Gamma(k + x)   k   x
          =  ------------  q   p
             Gamma(k) x!

where p = m / (k + m) and q = 1 - p.

The estimation is carried out by nbreg. Its _b[_cons] is ln m and its
_b[/lnalpha] is ln(1 / k).


Option 

log specifies that the results of nbreg should be displayed.


Example

Hilborn and Mangel (1997, p.100) give data on incidental capture of albatrosses
in the New Zealand subantarctic squid trawl fishery, 1990. (The birds get
trapped accidentally in nets or trawl gear or cables.) The data are in
frequency distribution form:

    . input x freq
    1. 0 807
    2. 1 37
    3. 2 27
    4. 3 8
    5. 4 4
    6. 5 4
    7. 6 1
    8. 7 3
    9. 8 1
    10. 9 0
    11. 10 0
    12. 11 2
    13. 12 1
    14. 13 1
    15. 14 0
    16. 15 0
    17. 16 0
    18. 17 1
    19. end

    . nbfit x [w=freq]


Saved values 

    r(N)      number of values used
    r(mean)   ML estimate of m
    r(k)      ML estimate of k
    r(p)      ML estimate of p
    r(V)      variance-covariance matrix of (m,k,p) (delta method)

References 

Hilborn, R. and Mangel, M. 1997.  The ecological detective: confronting models
with data.  Princeton University Press, Princeton, NJ.

Krebs, C.J. 1999. Ecological methodology. Benjamin/Cummings, Menlo Park, CA.

Rice, J.A. 1995. Mathematical statistics and data analysis. Duxbury, Belmont,
CA.


Author

         Nicholas J. Cox, University of Durham, U.K.
         n.j.cox@durham.ac.uk

         Roberto G. Gutierrez, Stata Corporation
         rgutierrez@stata.com


Also see

On-line:  help for nbreg 
 Manual:  [R] nbreg