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Vigorish percentage for three-way events may be calculated using the following formula: [5] = / + / + / / + / + / where p, q and t are the decimal payouts for each outcome. For comparison, for over round calculation only the upper part of the equation is used, leading to slightly higher percentage results than the vigorish calculation.
These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where: E = (a + 4m + b) / 6 SD = (b − a) / 6. E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate.
Many object-oriented programming languages have a three-way comparison function, which performs a three-way comparison between the object and another given object. For example, in Java , any class that implements the Comparable interface has a compareTo method which either returns a negative integer, zero, or a positive integer, or throws a ...
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Gauss–Kronrod formulas are extensions of the Gauss quadrature formulas generated by adding + points to an -point rule in such a way that the resulting rule is exact for polynomials of degree less than or equal to + (Laurie (1997, p. 1133); the corresponding Gauss rule is of order ).
Composite Simpson's 3/8 rule is even less accurate. Integration by Simpson's 1/3 rule can be represented as a weighted average with 2/3 of the value coming from integration by the trapezoidal rule with step h and 1/3 of the value coming from integration by the rectangle rule with step 2h. The accuracy is governed by the second (2h step) term.
The simplest example given by Thimbleby of a possible problem when using an immediate-execution calculator is 4 × (−5). As a written formula the value of this is −20 because the minus sign is intended to indicate a negative number, rather than a subtraction, and this is the way that it would be interpreted by a formula calculator.
Extrapolated Runs (XR) is a baseball statistic invented by sabermetrician Jim Furtado to estimate the number of runs a hitter contributes to his team. XR measures essentially the same thing as Bill James' Runs Created, but it is a linear weights formula that assigns a run value to each event, rather than a multiplicative formula like James' creation.