American Journal of Theoretical and Applied Statistics

Volume 5, Issue 2, March 2016

  • Tolerance Limits on Order Statistics in Future Samples Coming from the Two-Parameter Exponential Distribution

    Nicholas A. Nechval, Konstantin N. Nechval

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 1-6
    Received: 9 September 2015
    Accepted: 10 September 2015
    Published: 30 November 2015
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    Abstract: This paper presents an innovative approach to constructing lower and upper tolerance limits on order statistics in future samples. Attention is restricted to invariant families of distributions under parametric uncertainty. The approach used here emphasizes pivotal quantities relevant for obtaining tolerance factors and is applicable whenever the s... Show More
  • Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability

    Nicholas A. Nechval, Konstantin N. Nechval

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 7-11
    Received: 9 September 2015
    Accepted: 10 September 2015
    Published: 30 November 2015
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    Abstract: In this paper, an efficient approach to pattern recognition (classification) is suggested. It is based on minimization of misclassification probability and uses transition from high dimensional problem (dimension p≥2) to one dimensional problem (dimension p=1) in the case of the two classes as well as in the case of several classes with separati... Show More
  • A New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data

    Nicholas A. Nechval, Gundars Berzins, Vadims Danovics

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 12-20
    Received: 2 November 2015
    Accepted: 2 November 2015
    Published: 30 November 2015
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    Abstract: Identifying the ‘right’ dose is one of the most critical and difficult steps in the clinical development process of any medicinal drug. Its importance cannot be understated: selecting too high a dose can result in unacceptable toxicity and associated safety problems, while choosing too low a dose leads to smaller chances of showing sufficient effic... Show More
  • Optimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach

    Nicholas A. Nechval, Gundars Berzins, Vadims Danovics

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 21-28
    Received: 7 January 2016
    Accepted: 8 January 2016
    Published: 27 January 2016
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    Abstract: Age replacement strategies, where a unit is replaced upon failure or on reaching a predetermined age, whichever occurs first, provide simple and intuitively attractive replacement guidelines for technical units. Within theory of stochastic processes, the optimal preventive replacement age, in the sense of leading to minimal expected costs per unit ... Show More
  • Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models

    Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 29-39
    Received: 17 January 2016
    Accepted: 19 January 2016
    Published: 4 February 2016
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    Abstract: The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a ... Show More
  • A Novel Approach to Finding Sampling Distributions for Truncated Laws Via Unbiasedness Equivalence Principle

    Nicholas A. Nechval, Sergey Prisyazhnyuk, Vladimir F. Strelchonok

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 40-48
    Received: 26 January 2016
    Accepted: 28 January 2016
    Published: 23 February 2016
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    Abstract: Truncated distributions arise naturally in many practical situations. In this paper, the problem of finding sampling distributions for truncated laws is considered. This problem concerns the very important area of information processing in Industrial Engineering. It remains today perhaps the most difficult and important of all the problems of mathe... Show More
  • Efficient Predictive Inferences for Future Outcomes Under Parametric Uncertainty of Underlying Models

    Nicholas A. Nechval, Natalija Ribakova, Gundars Berzins

    Issue: Volume 5, Issue 2-1, March 2016
    Pages: 49-55
    Received: 31 January 2016
    Accepted: 2 February 2016
    Published: 23 February 2016
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    Abstract: Predictive inferences (predictive distributions, prediction and tolerance limits) for future outcomes on the basis of the past and present knowledge represent a fundamental problem of statistics, arising in many contexts and producing varied solutions. In this paper, new-sample prediction based on a previous sample (i.e., when for predicting the fu... Show More