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Then is called a pivotal quantity (or simply a pivot). Pivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels.
A ancillary statistic is a specific case of a pivotal quantity that is computed only from the data and not from the parameters. They can be used to construct prediction intervals. They are also used in connection with Basu's theorem to prove independence between statistics. [4]
In their book Pivot Table Data Crunching, [2] Bill Jelen and Mike Alexander refer to Pito Salas as the "father of pivot tables". While working on a concept for a new program that would eventually become Lotus Improv, Salas noted that spreadsheets have patterns of data. A tool that could help the user recognize these patterns would help to build ...
The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958. [1] [2]
[1] [2] [3] Spreadsheets were developed as computerized analogs of paper accounting worksheets. [4] The program operates on data entered in cells of a table. Each cell may contain either numeric or text data, or the results of formulas that automatically calculate and display a value based on the contents of other cells.
This system has the exact solution of x 1 = 10.00 and x 2 = 1.000, but when the elimination algorithm and backwards substitution are performed using four-digit arithmetic, the small value of a 11 causes small round-off errors to be propagated. The algorithm without pivoting yields the approximation of x 1 ≈ 9873.3 and x 2 ≈ 4.
If we only consider the means, the paired and unpaired approaches give the same result. To see this, let Y i1, Y i2 be the observed data for the i th pair, and let D i = Y i2 − Y i1. Also let D, Y 1, and Y 2 denote, respectively, the sample means of the D i, the Y i1, and the Y i2. By rearranging terms we can see that
The bootstrap sample is taken from the original by using sampling with replacement (e.g. we might 'resample' 5 times from [1,2,3,4,5] and get [2,5,4,4,1]), so, assuming N is sufficiently large, for all practical purposes there is virtually zero probability that it will be identical to the original "real" sample. This process is repeated a large ...
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