Abstract
This paper is concerned with the exact distribution of argmax (argmin) of a sequence of random variables. By argmax (argmin), we mean the random variable which attains the maximum (minimum) of the sequence. Change point estimators are of this type and the asymptotic distribution of this kind of estimator is studied extensively in literature. However, the exact distributions is generally not considered. Therefore, this paper is devoted to the exact distributions of the argmax in case of several examples. Finally, an approximation method is proposed.
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