  The geometric sum plays a significant role in risk theory and reliability
theory \cite{Kala97} and a prototypical example of the geometric sum is
R\'enyi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised
geometric sums converges to the exponential distribution. There is extensive
study of the accuracy of exponential distribution approximation to the
geometric sum \cite{Sugakova95,Kala97,PekozRollin11} but there is little study
on its natural counterpart of gamma distribution approximation to negative
binomial sums. In this note, we show that a nonnegative random variable follows
a gamma distribution if and only if its size biasing equals its zero biasing.
We combine this characterisation with Stein's method to establish simple bounds
for gamma distribution approximation to the sum of nonnegative independent
random variables, a class of compound Poisson distributions and the negative
binomial sum of random variables.
