Journal ArticleDOI
Estimates of Bounded Relative Error for the Mean Life of an Exponential Distribution
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In this paper, an estimation procedure for the mean life 0 having a small relative error is presented, with some pre-assigned confidence 1 a, within a certain percentage (100 6 percent) of the true but unknown mean life.Abstract:
In this note we find an estimation procedure for the mean life 0 having a small relative error. Put more precisely, we show how to get an estimate which is, with some preassigned confidence 1 a, within a certain percentage (100 6 percent) of the true but unknown mean life 0. In the language of life testing, this will require observing a suitably large number of failures, r. The exact solution of the problem involves considerations like those in [1]. Suppose that a fixed number, r, of failures is observed, and suppose that the associated total life is T , then it can be shown that the "best" estimator of 0 in the minimax sense corresponding to the loss functionread more
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Describing the size of discontinuities
TL;DR: The trace lengths of discontinuities from Nchanga Open Pit are a sample from a censored negative exponential distribution as discussed by the authors, and the largest trace length of a discontinuity in the distribution can be estimated from the parameters of the distribution and is substantially larger than an estimate by another method.
Journal ArticleDOI
Maximum likelihood estimation of joint size from trace length measurements
Ernesto Villaescusa,E. T. Brown +1 more
TL;DR: In this article, a parametric model for the three-dimensional distribution of joint sizes is developed under the assumptions of joint convexity and circularity, which best reflects the observed joint trace data, and corrects simultaneously for joint censoring, truncation and size bias.
Journal ArticleDOI
A Survey of Maximum Likelihood Estimation
TL;DR: A survey of the development of the theory of Maximum Likelihood Estimation (MLE) since its introduction in the papers of Fisher (1922, 1925) up to the present day where original work in this field still continues is given in this paper.
Journal ArticleDOI
Optimal Monte Carlo integration with fixed relative precision
TL;DR: An inequality for the mean square error of randomly stopped sums is proved and a lower bound on the worst case complexity of the (@e,@a)-approximation is derived.
Journal ArticleDOI
Exact sample size determination in a weibull test plan when there is time censoring
TL;DR: In this article, a new procedure based on both simulation and asymptotic theory is proposed to determine the sample size for a test plan, which is based on the property that the distribution of the t-like quantities is close to the standard normal in large samples.
References
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Journal ArticleDOI
Estimates of Bounded Relative Error in Particle Counting
TL;DR: In this article, a sampling procedure is proposed in which the continuous variable is observed until a fixed number $M$ of events occurs, which enables us to form an estimate $l$, which with confidence coefficient $\alpha$ does not differ from $\lambda$ by more than 100 $\gamma$ per cent of $\lambda$.