Poisson inverse cumulative distribution function that returns k instead of m?

[Robert Martin]

Hello,

Stata's invpoisson() function "returns the Poisson mean such that the cumulative Poisson distribution evaluated at k is p: if poisson(m,k) = p, then invpoisson(k,p) = m," according to the user guide. Is there an inverse Poisson CDF function that returns k for a given (m,p)? I understand the difficulty in inverting the Poisson CDF, but R has this function (QPOIS), so I thought it might be possible in Stata.

Thanks for your time,

Bob

[Scott Merryman]

This is adapted from:
http://www.mrexcel.com/forum/excel-q...e-poisson.html

discard
capture program drop invpoisk
*For a Poisson process with mean m
*returns the largest integer such that the CDF <= p
*E.g.,  disp %18.15f poisson(10,5) returns 0.067085962879032
*invpoisk(10, 0.067085962879032) returns 5
*Adapted from http://www.mrexcel.com/forum/excel-questions/507508-reverse-poisson.html

program invpoisk, rclass
syntax ,[ m(real 1) p(real 1)]
    scalar dm = exp(-`m')
    scalar dCDF = 0
    scalar dFact =1
    scalar dPower = 1
    scalar iX = 0
    while dCDF < `p' {
        scalar dCDF = dCDF + dm*dPower/ dFact
        scalar iX = iX + 1
        scalar dFact = dFact* iX
        scalar dPower = dPower * `m'
    }
    scalar k = iX - cond(dCDF/`p' >1, 2,1)
    return scalar k = k
    disp "k = " k " for a given mean and probability(`m', `p')"
end

. invpoisk, m(10) p(.067085962879032)
k = 5 for a given mean and probability(10, .067085962879032)

. invpoisk, m(4.28) p(.2)
k = 2 for a given mean and probability(4.28, .2)

[Robert Martin]

This is awesome. Thank you for your help!

-Bob