The Reciprocal of the Decapitated Negative Binomial Variable
Zakkula Govindarajulu · Journal of the American Statistical Association · 1962
The i-th inverse moment of a decapitated negative binomial variable is expressed as an integral, the integrand of which involves its (i − 1)th inverse moment. A bound on the cumulative round off error involved in using the recurrent formulae for the inverse moments of the decapitated negative binomial variable is obtained. The cumulative error is found to be not serious. Various approximations for these moments have also been obtained. Among these, the gamma approximations seem to be accurate to two or more decimal places for values of m and p such that mp > 5, provided the gamma approximations are applicable. An application of these moments is also considered.