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Technical formulation of the Hill's estimator is as follows. For , write () for the -th largest value of ,,. Then, with this notation, the Hill's estimator (see page 190 of Reference 5 by Embrechts et al ) based on the upper order statistics is defined as
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The distribution of a random variable X with distribution function F is said to have a long right tail [1] if for all t > 0, [> + >] =,or equivalently ¯ (+) ¯ (). This has the intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level.
Prominence calculations may use the high contour (giving in a pessimistic estimate [10] [11]), the low contour (giving an optimistic estimate), their mean (giving a "midrange" or "rise" prominence [12]) or an interpolated value (customary in Britain). The choice of method depends largely on the preference of the author and historical precedent.
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The Hill equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand. [1] [2] [nb 1] This equation is formally equivalent to the Langmuir isotherm. [3] Conversely, the Hill equation proper reflects the cellular or tissue response to the ligand: the physiological output of the system, such as muscle ...
To compare each estimator tool below, we’ll use the same example property and run it through each tool to see how the results compare. Our example property is 303 Willowcrest Drive, a 4-bedroom ...
d = run Δh = rise l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent.