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Bootstrapped tests for epistemic fuzzy data

Grzegorzewski Przemyslaw, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 2

277--289

Epistemic bootstrap is a resampling algorithm that generates bootstrap real-valued samples based on some epistemic fuzzy data input. We apply this method as a universal basis for various statistical tests which can be then directly used for fuzzy random variables. Two classical goodness-of-fit tests are considered as an example to examine the suggested methodology for both synthetic and real data. The proposed approach is also compared with two other goodness-of-fit tests dedicated directly to fuzzy data.

Temperature detection based on nonparametric statistics of ultrasound echoes

Byra M., Gambin B.

Hydroacoustics

2015

Vol. 18

17—23

Different ultrasound echoes properties have been used for the noninvasive temperature monitoring. Temperature variations that occur during heating/cooling process induce changes in a random process of ultrasound backscattering. It was already proved that the probability distribution of the backscattered RF (radio frequency) signals is sensitive to the temperature variations. Contrary to previously used methods which explored models of scattering and involved techniques of fitting histograms to a special probability distribution two more direct measures of changes in statistics are proposed in this paper as temperature markers. They measure the ''distance'' between the probability distributions. The markers are the Kolmogorov Smirnov distance and Kulback-Leiber divergence. The feasibility of using such nonparametric statistics for non- invasive ultrasound temperature estimation is demonstrated on the ultrasounds data collected during series of heating experiments in which the temperature was independently registered by the classical thermometer or thermocouples.

Statistical inference about the median from vague data

Grzegorzewski P.

Control and Cybernetics

1998

Vol. 27, no 3

447-464

In traditional statistics all parameters of the mathematical model and possible observations should be well defined. Sometimes such assumption appears too rigid for the real-life problems, especially when dealing with imprecise or linguistic data. To relax this rigidity fuzzy methods are incorporated into statistics. This paper is devoted to statistical inference about the population median in the presence of vague data. We propose the notion of fuzzy median. Then we suggest a fuzzy estimator and fuzzy confidence interval for the median. Next we discuss the problem of hypothesis testing concerning the median in the presence of imprecise data. All methods presented are distribution-free.