Regenerative Simulation for Estimating Extreme Values

Article Abstract:

The estimation of the extreme values of the regenerative process is studied. The paper develops a method for estimating the distribution of X*(t). When the regenerative process is either the GI-G-1 queue or a birth-death process, theoretical results are available for the distribution of X*(t). The waiting time, queue length, and virtual waiting time for an M-M-1 queue is simulated. It employed the method for estimating the distribution of X*(t), and the results are compared with theoretical results. Tables presenting computational results are included.

Queuing theory, Simulation, Estimation, Simulation Theory, Statistical Analysis, Theory, Discrete Mathematics

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The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function under Liner Constraints

Article Abstract:

The minimum value of a sample of feasible points uniformly distributed over a linear constraint set is for concave functions, asymptotically Weibull-distributed. Its shape parameter is equal to the dimension of the feasible region. This result is distinguished by the property that the particular member of the family of extreme value distributions, which the sample minimum converges to, is uniquely determined by the geometry of the constraint set.

Mathematical models

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Selecting an Extreme-Value Distribution and the Transforming to a Specified Distribution

Article Abstract:

In statistics, it is common to take square roots, logarithms, or otherwise transform data in order to improve the assumption of normality. Extreme value distributions often are candidates for life-length distributions. To transform these distributions to a standard exponential is analogous to selecting the best fit distributions from the collection of extreme value distributions. Examples are given.

Reliability (Trustworthiness), Curve fitting, Reliability, Mathematics of Computing, Transforms, Bayesian Theory

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