Rectangular Distribution Whose Width is Not Exactly Known: Isocurvilinear Trapezoidal Distribution

Published

June 1, 2009

Author(s)

Raghu N. Kacker, James F. Lawrence

Abstract

After the Gaussian distribution, the probability distribution most commonly used in evaluating uncertainty in measurement is the rectangular distribution. When the mid-point of a rectangular distribution is fixed but the half-width is uncertain and the probability distribution of the half-width can be represented by another rectangular probability distribution, the resulting distribution looks like a trapezoid whose sloping sides are curved. We can refer to such a distribution as curvilinear trapezoidal distribution. A symmetric curvilinear trapezoid is isocurvilinear. We discuss the properties of an isocurvilinear trapezoidal distribution which arises when the probability distribution of the half-width can be represented by another rectangular distribution. When the uncertainty in half-width is not excessive, the isocurvilinear trapezoidal distribution is well approximated by an isosceles trapezoidal distribution.

Citation

Metrologia

Volume

46

Issue

3

Pub Type

Journals

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Keywords

trapezoidal distribution, uncertainty in measurement

Citation

Kacker, R. and Lawrence, J. (2009), Rectangular Distribution Whose Width is Not Exactly Known: Isocurvilinear Trapezoidal Distribution, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=890099 (Accessed March 14, 2025)