Evidential inference and optimal sample size determination on the basis of record values and record times under random sampling scheme

In this paper, the likelihood ratio approach is applied for measuring evidence provided by record data in favor of a hypothesis against an alternative under a random sampling scheme. Explicit expressions for probabilities of observing strong and weak evidences are derived. Asymptotic behaviors of these probabilities are investigated in a greater detail. Optimal sample size in which the substantial evidence reaches a desired level is determined. An illustrative example concerning records of times between consecutive telephone calls to a company’s switchboard is also analyzed.