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The elements of a dispersion fan diagram [1] are: a circular line as scale; a diameter which indicates the median; a fan (a segment of a circle) which indicates the quartiles; two feathers which indicate the extreme values. The scale on the circular line begins at the left with the starting value (e. g. with zero). The following values are ...
Hyndman's MASE metric resolves these and can be used under any forecast generation method. [6] It allows for comparison between models due to its scale-free property. Hyndman studied statistics and mathematics at the University of Melbourne, where he earned a Bachelor of Science with first class honours and a PhD. [1]
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Hyndman and Fan compiled a taxonomy of nine algorithms [2] used by various software packages. All methods compute Q p, the estimate for the p-quantile (the k-th q-quantile, where p = k/q) from a sample of size N by computing a real valued index h. When h is an integer, the h-th smallest of the N values, x h, is the quantile estimate.
Percentile scores and percentile ranks are often used in the reporting of test scores from norm-referenced tests, but, as just noted, they are not the same. For percentile ranks, a score is given and a percentage is computed. Percentile ranks are exclusive: if the percentile rank for a specified score is 90%, then 90% of the scores were lower.
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Percentile ranks are not on an equal-interval scale; that is, the difference between any two scores is not the same as between any other two scores whose difference in percentile ranks is the same. For example, 50 − 25 = 25 is not the same distance as 60 − 35 = 25 because of the bell-curve shape of the distribution. Some percentile ranks ...
The area arose owing to the emergence of many modern data sets in which the dimension of the data vectors may be comparable to, or even larger than, the sample size, so that justification for the use of traditional techniques, often based on asymptotic arguments with the dimension held fixed as the sample size increased, was lacking. [1] [2]
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