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The present paper discusses the statistical distribution for the estimator ofRosenthal's 'Fail-Safe' number NR, which is an estimator of unpublished studiesin meta-analysis. We calculate the probability distribution function of NR.This is achieved based on the Central Limit Theorem and the proposition thatcertain components of the estimator NR follow a half normal distribution,derived from the standard normal distribution. Our proposed distributions aresupported by simulations and investigation of convergence.

Exploring the Distribution for the Estimator of Rosenthal's 'Fail-Safe' Number of Unpublished Studies in Meta-analysis