### About a fixed precision estimation of the parameter of uniform density

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The object of this paper is to survey the methods of fixed precision estimation of the maximal value of a bounded random variable. In particular the paper gives solutions to this problem for a class of distributions with unknown scale parameter (section 2) and for a class of distributions with certain features of symmetry (section 3). The sequential procedures solving both subproblems are not only asymptotically consistent and asympto-tically efficient in the sense of Chow and Robbins (like that...

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Optimal stopping time problems for a risk process ${U}_{t}=u+ct-{\sum}_{n=0}^{N\left(t\right)}{X}_{n}$ where the number N(t) of losses up to time t is a general renewal process and the sequence of ${X}_{i}$’s represents successive losses are studied. N(t) and ${X}_{i}$’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

The article contains no abstract

The article contains no abstract

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