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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.
On the other hand, in its version for identifying power-law probability distributions, the mean residual life plot consists of first log-transforming the data, and then plotting the average of those log-transformed data that are higher than the i-th order statistic versus the i-th order statistic, for i = 1, ..., n, where n is the size of the ...
In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a parametric test and a nonparametric test of the same hypothesis. Tests may have the same size , and hence the same false positive rates, but different ability to detect true effects.
Some examples follow. Priestley uses stationary up to order m if conditions similar to those given here for wide sense stationarity apply relating to moments up to order m. [3] [4] Thus wide sense stationarity would be equivalent to "stationary to order 2", which is different from the definition of second-order stationarity given here.
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). This is also known as the rank–frequency distribution, when the source data are from a frequency distribution. These ...
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, the ranks of the numerical data 3.4, 5.1, 2.6, 7.3 are 2, 3, 1, 4. As another example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.
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 ...
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...