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Order statistics have a lot of applications in areas as reliability theory, financial mathematics, survival analysis, epidemiology, sports, quality control, actuarial risk, etc. There is an extensive literature devoted to studies on applications of order statistics in these fields.
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities.
The main application of statistical power is "power analysis", a calculation of power usually done before an experiment is conducted using data from pilot studies or a literature review. Power analyses can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size (in other ...
A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language. The Zipf–Mandelbrot law is a discrete power law distribution which is a generalization of the Zipf distribution. Conway–Maxwell–Poisson distribution Poisson distribution Skellam distribution
It is usually determined on the basis of the cost, time or convenience of data collection and the need for sufficient statistical power. For example, if a proportion is being estimated, one may wish to have the 95% confidence interval be less than 0.06 units wide. Alternatively, sample size may be assessed based on the power of a hypothesis ...
Rank–size distribution is the distribution of size by rank, in decreasing order of size. For example, if a data set consists of items of sizes 5, 100, 5, and 8, the rank-size distribution is 100, 8, 5, 5 (ranks 1 through 4).
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A bump chart—a line chart that shows the relative ranking of items from one time point to the next—is also appropriate for ordinal data. [14] Color or grayscale gradation can be used to represent the ordered nature of the data. A single-direction scale, such as income ranges, can be represented with a bar chart where increasing (or ...