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The Bayes choice of an experiment in estimating a success probability

Alicja Jokiel-Rokita, Ryszard Magiera (2002)

Applicationes Mathematicae

A Bayesian method of estimation of a success probability p is considered in the case when two experiments are available: individual Bernoulli (p) trials-the p-experiment-or products of r individual Bernoulli (p) trials-the p r -experiment. This problem has its roots in reliability, where one can test either single components or a system of r identical components. One of the problems considered is to find the degree r̃ of the p r ̃ -experiment and the size m̃ of the p-experiment such that the Bayes estimator...

The Bayes sequential estimation of a normal mean from delayed observations

Alicja Jokiel-Rokita (2006)

Applicationes Mathematicae

The problem of estimating the mean of a normal distribution is considered in the special case when the data arrive at random times. Certain classes of Bayes sequential estimation procedures are derived under LINEX and reflected normal loss function and with the observation cost determined by a function of the stopping time and the number of observations up to this time.

The stability of parameter estimation of fuzzy variables

Dug Hun Hong (2009)

Kybernetika

Recently, the parameter estimations for normal fuzzy variables in the Nahmias’ sense was studied by Cai [4]. These estimates were also studied for general T -related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.

The "Thirty-seven Percent Rule" and the secretary problem with relative ranks

Béla Bajnok, Svetoslav Semov (2014)

Discussiones Mathematicae Probability and Statistics

We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank;...

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