Exploring the distribution for the estimator of Rosenthal's fail-safe' number of unpublished studies in meta-analysis

The present article discusses the statistical distribution for the estimator of Rosenthal's file-drawer' number N-R, which is an estimator of unpublished studies in meta-analysis. We calculate the probability distribution function of N-R. This is achieved based on the central limit theorem and the proposition that certain components of the estimator N-R follow a half-normal distribution, derived from the standard normal distribution. Our proposed distributions are supported by simulations and investigation of convergence.