In this chapter we illustrate the use of the methodology of sample path analysis for deriving the exact distributions of sampling size (stopping times) in two-stage and sequential estimation of the parameters of distributions, with precision requirements, like fixed-width confidence intervals or bounded risk estimators. We show here two cases, the estimation of the scale parameter of an exponential distribution, and the estimation of the log-odds in Bernoulli trials. The following references are for other papers in which the same methods were used: De (2014); De and Mukhopadhyay (2015); Haner and Zacks (2013); Mahmoudi and Roughani (2015); Roughani and Mahmoudi (2015); Zacks and Khan (2011); Zacks (2009, 2015).
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