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The area under the effect curve (AUEC) is an integral of the effect of a drug over time, estimated as a previously-established function of concentration. It was proposed to be used instead of AUC in animal-to-human dose translation, as computer simulation shows that it could cope better with half-life and dosing schedule variations than AUC.
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96 , meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean .
Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
This can also be seen from the geometric picture: the trapezoids include all of the area under the curve and extend over it. Similarly, a concave-down function yields an underestimate because area is unaccounted for under the curve, but none is counted above. If the interval of the integral being approximated includes an inflection point, the ...
Taking an example, the area under the curve y = x 2 over [0, 2] can be procedurally computed using Riemann's method. The interval [0, 2] is firstly divided into n subintervals, each of which is given a width of 2 n {\displaystyle {\tfrac {2}{n}}} ; these are the widths of the Riemann rectangles (hereafter "boxes").
In a graphical representation of the continuous uniform distribution function [()], the area under the curve within the specified bounds, displaying the probability, is a rectangle. For the specific example above, the base would be 16 , {\displaystyle 16,} and the height would be 1 23 . {\displaystyle {\tfrac {1}{23}}.} [ 5 ]
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The peak is "well-sampled", so that less than 10% of the area or volume under the peak (area if a 1D Gaussian, volume if a 2D Gaussian) lies outside the measurement region. The width of the peak is much larger than the distance between sample locations (i.e. the detector pixels must be at least 5 times smaller than the Gaussian FWHM).