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A homogeneous Poisson process (N(t), t ≥ 0) with the intensity function m(t) = θ is observed on the interval [0, T ]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T . The optimal T is given when the prior distribution of θ is not uniquely specified.

Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior