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The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings.
Empirically, a data set can be tested to see whether Zipf's law applies by checking the goodness of fit of an empirical distribution to the hypothesized power law distribution with a Kolmogorov–Smirnov test, and then comparing the (log) likelihood ratio of the power law distribution to alternative distributions like an exponential ...
It examines the share of the relevant product category sold by stores in which a given product has gained distribution. [1] Distribution metrics quantify the availability of products sold through retailers, usually as a percentage of all potential outlets. Often, outlets are weighted by their share of category sales or “all commodity” sales.
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
All-commodity volume (ACV) is a weighted measure of product availability, or distribution, based on total store sales. In other words, ACV is the percentage of sales in all categories that are generated by the stores that stock a given brand (again, at least one SKU of that brand) (note: ACV can be expressed as a percentage or as a dollar value (total sales of stores carrying brand).
In the financial field, and more specifically in the analyses of financial data, a weighted moving average (WMA) has the specific meaning of weights that decrease in arithmetical progression. [4] In an n -day WMA the latest day has weight n , the second latest n − 1 {\displaystyle n-1} , etc., down to one.
The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. Modified duration is the name given to the price ...
The Lorenz curve is a probability plot (a P–P plot) comparing the distribution of a variable against a hypothetical uniform distribution of that variable. It can usually be represented by a function L ( F ), where F , the cumulative portion of the population, is represented by the horizontal axis, and L , the cumulative portion of the total ...