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In order to answer this question, uncertain statistics was firstly presented by Liu in 2010, and is a methodology for collecting and interpreting expert’s experimental data by uncertainty theory.
#Method of moments how to
One important issue in uncertainty theory is how to determine uncertainty distribution of an uncertain variable. For exploring the recent developments of uncertainty theory, the readers may consult the book. Nowadays, uncertainty theory was well developed on both theory section and practice section. Other references related to uncertainty theory are Gao, Gao et al. Meanwhile, as an application of uncertainty theory, Liu proposed a spectrum of uncertain programming and applied uncertain programming to system reliability design, facility location problem, vehicle routing problem, project scheduling problem, and so on. Based on Liu’s uncertainty theory, some basic and important theoretical work of uncertainty theory such as uncertain process, uncertain calculus, uncertain differential equation, uncertain logic, uncertain inference, and uncertain risk analysis have been established. In order to model this type of imprecise quantities, uncertainty theory was founded by Liu in 2007 and refined by Liu in 2010 and became a branch of mathematics based on the normality, duality, subadditivity, and product axioms.
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However, the examples tell us that it is inappropriate because probability theory and fuzzy set theory may lead to counterintuitive results in this case. Perhaps some people think that the belief is a subjective probability or fuzzy membership degree. Since human beings usually overweigh unlikely events, the belief degree may have much larger variance than the real frequency. When the sample size is too small (even no-sample) to estimate a probability distribution, we have to invite some domain experts to evaluate their belief degree that each event will occur. However, a lot of surveys showed that some information and knowledge represented usually by human language like ‘about 1,000 km,’ ‘roughly 60 kg,’ ‘high speed,’ and ‘small size’ are neither randomness nor fuzziness. In order to determine the membership function, fuzzy statistics was presented including fuzzy point estimation by a fuzzy decision-making approach and so on. On the other hand, the fuzzy set theory via membership function initiated by Zadeh is a mathematical model of vague qualitative or qualitative data, frequently generated by means of natural language. In order to determine the probability distribution, random statistics (i.e., the classical mathematical statistics) was proposed as a methodology for collecting and interpreting the test data with correlative information in a system by probability theory. The probability distribution describes the range of possible values and the probability of a random variable. Probability theory is a branch of mathematics concerned with analysis of random phenomena.