Prediction intervals are increasingly recommended in random-effects meta-analysis because they describe the range of true effects expected in a future study or setting. Conventional frequentist intervals can have inadequate finite-sample coverage because uncertainty in the between-study variance is not fully propagated. We propose a confidence-distribution propagation method that carries uncertainty through the random-effects hierarchy. The method samples the between-study variance from a confidence distribution obtained by inverting the exact distribution of Cochran's Q and, conditional on each draw, samples the average effect from its corresponding normal confidence distribution before generating a future true effect. Prediction limits are empirical quantiles of the resulting Monte Carlo distribution. Across the scenarios examined, the proposed method improved or maintained coverage relative to existing frequentist intervals, including the Nagashima-Noma-Furukawa confidence-distribution bootstrap, with generally modest increases in expected width. The same Monte Carlo sample also yields confidence intervals for the average effect and heterogeneity measures. The method is implemented in the R package cdmeta available at CRAN (https://doi.org/10.32614/CRAN.package.cdmeta).

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