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How To Describe Measurement Errors: A Natural Generalization Of The Central Limit Theorem Beyond Normal (And Other Infinitely Divisible) Distributions, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When precise measurement instruments are designed, designers try their best to decrease the effect of the main factors leading to measurement errors. As a result of this decrease, the remaining measurement error is the joint result of a large number of relatively small independent error components. According to the Central Limit Theorem, under reasonable conditions, when the number of components increases, the resulting distribution tends to Gaussian (normal). Thus, in practice, when the number of components is large, the distribution is close to normal -- and normal distributions are indeed ubiquitous in measurements. However, in some practical situations, the distribution …