##Statistics Seminar##\\ Department of Mathematics and Statistics ^ **DATE:**|Thursday, February 8, 2024 | ^ **TIME:**|1:15pm -- 2:15pm | ^ **LOCATION:**|WH 100E | ^ **SPEAKER:**|Zhongyuan Zhao, Binghamton University | ^ **TITLE:**|Analytic Formulae for the Minimax Characteristics of the Generalized Shiryaev–Roberts Quickest Change-Point Detection Procedure under Exponential Observations | \\ **Abstract** We derive analytically exact closed-form formulae for a host of performance characteristics delivered by the Generalized Shiryaev–Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure’s headstart is not restricted to a bounded range, nor is there a “ceiling” value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.