## Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity (2006)

Venue: | Reliable Computing |

Citations: | 41 - 40 self |

### BibTeX

@ARTICLE{Kreinovich06towardscombining,

author = {V. Kreinovich and G. Xiang and S. A. Starks and L. Longpré and M. Ceberio and R. Araiza and J. Beck and A. Nayak and R. Torres and J. G. Hajagos},

title = {Towards combining probabilistic and interval uncertainty in engineering calculations: algorithms for computing statistics under interval uncertainty, and their computational complexity},

journal = {Reliable Computing},

year = {2006},

volume = {2006},

pages = {471--501}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data. In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.

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Citation Context ...ime of this algorithm is O(n · log(n)). Comment. In our proof, we used a technique of replacing two values in such a way that their sum (and hence, the overall average) remain unchanged. According to =-=[13]-=-, this technique, called a transfer, was first introduced by Robert Muirhead in 1903. The transfer technique is actively used both in mathematics, where it is one of the main tools in proving inequali... |

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