| 1. |
- Belyaev, Yu. K., et al.
(author)
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Analysis of survey data containing rounded censoring intervals
- 2015
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In: Informatika i ee primeneniâ. - : Federal Research Center "Computer Science and Control" of Russian Academy of Sciences. - 1992-2264 .- 2310-9912. ; 9:3, s. 2-16
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Journal article (peer-reviewed)abstract
- This paper makes a contribution towards the statistical analysis of data sets containing intervals, that naturally arises in survey contexts. The suggested approach is sufficiently general to cover most cases where interval data are used. Interval data appear in many contexts, such as in reliability studies and survival analysis, in medicine and economics, in opinion elicit surveys, etc. There are several reasons for the extensive use of interval data, perhaps, the most common being one of necessity; exact values of the underlying observations are censored. The nature of the intervals analyzed here is somewhat unusual. The self-selected intervals (SeSeI) are (freely) chosen by the subjects. A generalization of the influential approach has been suggested to the statistical analysis of general censoring introduced by B. W. Turnbull. A key independence assumption in Turnbull's analysis has been explained and generalized. A sampling stopping rule based on the coverage probability has been suggested and the properties of a two-step estimator, based on the idea of asking two questions, where the second involves a way of fine-graining the information, has been discussed. This paper provides several informatics methods for SeSeI, targeting the problem of partial nonparametric identification. The properties of the suggested statistical models are stated, including a recursion for easy numerical calculations. An extensive simulation study, displaying, inter alia, the usefulness of the proposed resampling methods for the situation under study, completes the paper.
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| 2. |
- Belyaev, Yu. K., et al.
(author)
-
Kolmogorov Stories
- 2021
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In: Probability in the engineering and informational sciences (Print). - : Cambridge University Press. - 0269-9648 .- 1469-8951. ; 35:3, s. 355-368
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Journal article (peer-reviewed)abstract
- Authors of this paper were educated and have spent many years in Lomonosov Moscow State University (MSU), in the Interfaculty Laboratory of Statistical Methods (ILSM). Prof. Yu. K. Belyaev was student of Kolmogorov, and for several years his deputy in the ILSM, created and led by the great A. N. Kolmogorov. Now Prof. Yuri Belyaev is Emeritus Professor at Umea University (Sweden). Asaf Hajiyev was a PhD student in Kolmogorov's ILSM. In this paper some unusual incidents about the legendary Kolmogorov, and people around him are presented. Some stories were taken from the books and the internet (see references) dedicated to the memory of Kolmogorov; some were told by his students, and some happened with authors of this paper.
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| 3. |
- Belyaev, Yu. K., et al.
(author)
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Mathematical models of systems with several lifts and various control rules
- 2020
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In: Reliability. - 1932-2321. ; 15:2, s. 21-35
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Journal article (peer-reviewed)abstract
- In the present paper, several mathematical models of lifts’ systems with various control rules are constructed and simulated data are used for estimating the various parameters of the systems. For systems with a rare input flow of customers, the graphs, describing the positions of the lifts, at the preceding customer’s arrival instant, are given. These graphs help analytically find, the various characteristics of the lifts’ systems (a customer’s average waiting time, a customer’s total time, energy expenses and others). There are introduced the various control rules by the lift systems, which are investigated by simulation. Using Wolfram Mathematica, the authors have prepared several programs for simulating and estimating the various operational parameters of the lifts’ systems with different control rules. Using these programs, the numerical estimates of the various parameters the considered lifts’ systems, have been found. These data can be used for defining the dependence of optimal lift roominess on an intensity of input customers’ flow and finding the optimal number of the lifts, during planning and construction of the buildings and skyscrapers.
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| 4. |
- Belyaev, Yu.K., et al.
(author)
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On Non-Parametric Estimation of Poission Point Processes Related to Failure Stresses of Fibres
- 2000
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Reports (other academic/artistic)abstract
- We consider statistical analysis of the reliability of fibres. The problem is to estimate the distribution law of random failure stresses of fibres (i.e. the critical level of stresses that destroy fibres) by using data obtained in a special kind of test, where several fibres are tested until they break. All new pieces resulting from this test will also be tested, if they are long enough. The test ends when all the remaining pieces are too short to be tested further. We refer to these as binary tree structured tests. We assume that the cumulative hazard function (c.h.f.) of the failure stresses of these fibres is continuous, and that the fibres are statistically identical. Under these assumptions we obtain, as the number of tested fibres increases, a strongly consistent Nelson-Aalen type estimator of the c.h.f. The functional central limit resampling theorem in Skorohod space is proved. It justifies the possibility of using resampling for estimating the accuracy of these estimators. The theorem shows that resampling can be used to asymptotically consistently estimate distribution laws of continuous functionals of the random deviations between the estimator and the true c.h.f.. For example, resampling can be used to estimate the distribution law of the maximum distance between estimators and estimands. Numerical examples suggest that resampling works well for a moderate number of tested fibres.
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| 5. |
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| 6. |
- Rydén, Patrik, et al.
(author)
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The HRD-Algorithm : a general method for parametric estimation of two-component mixture models
- 2017
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In: Lecture Notes in Computer Science. - Cham : Springer. - 0302-9743 .- 1611-3349. ; 10684, s. 497-508
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Journal article (peer-reviewed)abstract
- We introduce a novel approach to estimate the parameters of a mixture of two distributions. The method combines a grid approach with the method of moments and can be applied to a wide range of two-component mixture models. The grid approach enables the use of parallel computing and the method can easily be combined with resampling techniques. We derive the method for the special cases when the data are described by the mixture of two Weibull distributions or the mixture of two normal distributions, and apply the method on gene expression data from 409 ER+" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ER+ER+ breast cancer patients.
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