In this post the contents of the book "Introduction to Sub-Interval Analysis and its Applications" are briefly reviewed in the Russian language, for the convenience of Russian and Russian-speaking readers.

This short paper is devoted to two items: 1) An analysis of Prelec’s weighting function at the probability p = 1 is highlighted (this analysis was performed by R. Duncan Luce in two articles with Ragnar Steingrimsson and János Aczél and here is referred to as the “Luce problem”). 2) The...

The article represents a brief review and development of the plenary report in the Moscow Institute of Physics and Technology. Three existing tools of sub-interval analysis (sub-interval arithmetic, incomplete data analysis and images) are reviewed and elements of two new tools (sub-interval...

В настоящей заметке, для удобства российских и русскоговорящих читателей, на русском языке кратко рассмотрено содержание книги "Введение в Суб-Интервальный...

Control charts are extensively used in many real world applications. Since process parameters are rarely known common practice is to estimate them. Then, the control limits are modified and become actually random variables. In this paper, we deal with the univariate control charts for dispersion...

The proof of the theorem of existence of the ruptures, namely the proof of maximality, is improved. The theorem may be used in economics and explain the well-known problems such as Allais’ paradox. Illustrated examples of ruptures are presented.

A theorem of existence of ruptures in the probability scale has been proven. The theorem can be used, e.g., in economics and forecasting. It can assist to solve paradoxes such as Allais paradox and the “four-fold-pattern” paradox and to create the correcting formula of forecasting.

The Shewhart and the Bonferroni-adjustment R and S chart are usually applied to monitor the range and the standard deviation of a quality characteristic. These charts are used to recognize the process variability of a quality characteristic. The control limits of these charts are constructed on...

In this paper, an evaluation method is suggested for selecting one of two competing models based on certain predictive ability ratings. The main focus is on the case of linear models that are not necessarily nested. In the context of such models, the test procedure is based on a sample statistic...

Measurements are frequently recorder without their algebraic sign. As a consequence the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is t the resulting distribution is called the “folded-t distribution”. Here...