During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration.

Meta-analyses combine the estimators of individual means to estimate the common mean of a population. However, the common mean could be undefined or uninformative in some scenarios where individual means are “ordered” or “sparse”. Hence, assessments of individual means become relevant, rather than the common mean. In this article, we propose simultaneous estimation of individual means using the James–Stein shrinkage estimators, which improve upon individual studies’ estimators. We also propose isotonic regression estimators for ordered means, and pretest estimators for sparse means. We provide theoretical explanations and simulation results demonstrating the superiority of the proposed estimators over the individual studies’ estimators. The proposed methods are illustrated by two datasets: one comes from gastric cancer patients and the other from COVID-19 patients.

Meta-analysis is an indispensable tool for synthesizing statistical results obtained from individual studies. Recently, non-Bayesian estimators for individual means were proposed by applying three methods: the James–Stein (JS) shrinkage estimator, isotonic regression estimator, and pretest (PT) estimator. In order to make these methods available to users, we develop a new R package meta.shrinkage. Our package can compute seven estimators (named JS, JS+, RML, RJS, RJS+, PT, and GPT). We introduce this R package along with the usage of the R functions and the “average-min-max” steps for the pool-adjacent violators algorithm. We conduct Monte Carlo simulations to validate the proposed R package to ensure that the package can work properly in a variety of scenarios. We also analyze a data example to show the ability of the R package.

Fixed-effect meta-analyses aim to estimate the common mean parameter by the best linear unbiased estimator. Besides unbiasedness, consistency is one of the most fundamental requirements for the common mean estimator to be valid. However, conditions for the consistency of the common mean estimator have not been discussed in the literature. This article fills this gap by clarifying conditions for making the common mean estimator consistent in fixed-effect meta-analyses. In this article, five theorems are devised, which state regularity conditions for the common mean estimator to be consistent. These theorems are novel applications of the classical large sample theory to meta-analyses. Numerical illustrations are also given to help understand the needs of the regularity conditions. Three real datasets illustrate the practical consequences of the devised theorems. This article concludes that the inconsistency of the common mean estimator occurs under some conditions in real meta-analyses.