  It is shown that the applicability conditions for the inverse Bernoulli
transform method for solving the inverse problem of photocount statistics are
determined by the fulfillment of the associativity condition for multiplying
the matrices included in this transformation. A general criterion for
evaluating the photocount distributions $Q_{m}$ in the case of few-photon
light, which makes it possible to establish whether the solution to the inverse
problem of photocount statistics by inverse Bernoulli transform method is
applicable for $\eta<0.5$, is found. As an example of application of the
obtained criterion, the critical quantum efficiency $\eta_{cr}$ is found for
compound Poisson distribution, below which the solution of the inverse problem
of photocount statistics becomes incorrect. Additionally it is shown that the
normalization of $Q_{m}$ is not sufficient to obtain a correct solution using
the inverse Bernoulli transform.
