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It is known that, if the mid-point of a rectangular distribution is specified, the half-width is inexactly known, and the state of knowledge about the half-width may be represented by a narrower rectangular distribution then the resulting distribution looks like an isosceles trapezoid whose sloping sides are curved (an isocurvilinear trapezoid). What sort of probability distribution must the half-width have for the resulting distribution to be an isosceles trapezoid? We show that if the distribution of the half-width is a variation of the rectangular distribution whose top is sloping (a sloping top distribution) then the resulting distribution is isosceles trapezoid.
Kacker, R.
and Lawrence, J.
(2010),
Derivation of Isosceles Trapezoidal Distribution, Measurement Science and Technology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=904335
(Accessed October 11, 2025)