Probabilistic distributions of ordinal statistics in the analysis of super-short fuzzy and incomplete time series

In a number of branches of scientific research, there is a problem of an estimate of rate of behavior of respondents under the incomplete and inexact initial data. Sources of such data can frequently be just statements of the respondent in a natural language, when such statements is the only mean to communicate knowledge about behavior. The calculate estimate of rate, as a rule, is used further for indirect estimate of other indicators.
Thus, an essential need arises for development of mathematical models (based, for example, on mathematical methods and objects from the area of soft calculations), allowing to pass from the limited number of inexact answers about last episodes of risky behavior, about the maximum, minimum and usual interval between episodes to an estimate of rate of the behavior, and to an indirect estimate of individual risk.
The paper pays the special attention to processing of answers of respondents with data on the maximum and minimum interval between episodes of risky behavior for the given period of time; several approaches to an estimate of the rate of risky behavior is offered. The approaches are based on construction and the analysis of functions of distributions and functions of joint distributions. Granulated (natural language discrepancy, an illegibility) initial data are processed with the method of N. V. Hovanov for the analysis and synthesis of aggregated indicators in case of information deficiency. Besides, interval estimate of rate are considered; the latter plays a special role in an estimate of “quality” of the scalar estimate.