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Probabilities, Intervals, What Next? Optimization Problems Related To Extension Interval Computations To Situations With Partial Information About Probabilities, Vladik Kreinovich
Probabilities, Intervals, What Next? Optimization Problems Related To Extension Interval Computations To Situations With Partial Information About Probabilities, Vladik Kreinovich
Departmental Technical Reports (CS)
When we have only interval ranges [xi-,xi+] of sample values x1,...,xn, what is the interval [V-,V+] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V+ is NP-hard. We provide a feasible (quadratic time) algorithm for computing the exact lower bound V- on the variance of interval data. We also provide feasible algorithms that computes V+ under reasonable easily verifiable conditions, in particular, in case interval uncertainty is introduced to maintain privacy in a statistical database.
We also extend the main formulas of interval arithmetic for different arithmetic operations …