Characteristic functions and effectiveness-of-fit test for uncertain distributions
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(College of Equipment Management and UAV Engineering, Air Force Engineering University, Xian 710051, China)

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O212.1

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    Abstract:

    Uncertainty theory is mainly used to deal with indeterminacy problems based on belief degree. In order to solve the problem of the lack of testing process after fitting uncertain distributions in practical application, characteristic functions with uncertain distributions were studied and effectiveness-of-fit test method was proposed. Firstly, the characteristic function of uncertain distribution was defined, and its calculation formula was given based on the uncertain expectation value. On the basis of the formula, the characteristic functions of several typical uncertain distributions were derived. Secondly, the properties of the characteristic functions were analyzed, which laid foundation for subsequent demonstration of theories and calculation. Thirdly, according to the definition and properties of the characteristic functions, the definition of effectiveness of uncertainty distribution fitting and its judgment theorem were proposed based on the digital characteristics and shape of distribution function. Finally, two examples were given to verify the feasibility and effectiveness of the proposed method. Simulation results show that uncertainty theory and stochastic theory are different in product axiom, and it is difficult to extend the method of distribution fitting test in stochastic theory to the uncertainty theory. In addition, there is a one-to-one correspondence between the uncertainty characteristic function and the uncertainty distribution function, and the uncertainty characteristic function can be used as one of the approaches to study the uncertainty distribution fitting test.

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History
  • Received:November 14,2017
  • Revised:
  • Adopted:
  • Online: April 12,2019
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