Rectangular distribution whose width is not exactly known: isocurvilinear trapezoidal distribution

Abstract

After the Gaussian distribution, the probability distribution most commonly used in evaluation of uncertainty in measurement is the rectangular distribution. If the half-width of a rectangular distribution is specified, the mid-point is uncertain, and the probability distribution of the mid-point may be represented by another (narrower) rectangular distribution then the resulting distribution is an isosceles trapezoidal distribution. However, in metrological applications, it is more common that the mid-point is specified but the half-width is uncertain. If the probability distribution of the half-width may be represented by another (narrower) rectangular distribution, then the resulting distribution looks like an isosceles trapezoid whose sloping sides are curved. We can refer to such a probability distribution as an isocurvilinear trapezoidal distribution. We describe the main characteristics of an isocurvilinear trapezoidal distribution which arises when the half-width is uncertain. When the uncertainty in specification of the half-width is not excessive, the isocurvilinear trapezoidal distribution can be approximated by an isosceles trapezoidal distribution.

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