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# Publication Citation: Rectangular Distribution Whose Width is Not Exactly Known: Isocurvilinear Trapezoidal Distribution

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Author(s): Raghu N. Kacker; James F. Lawrence; Rectangular Distribution Whose Width is Not Exactly Known: Isocurvilinear Trapezoidal Distribution June 01, 2009 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. Metrologia 46 3 pp. 254 - 260 trapezoidal distribution, uncertainty in measurement Math Click here to retrieve PDF version of paper (171KB)