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A New Statistical Tool: Scalar Score Function
Zdeněk Fabián
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DOI:10.17265/1934-7332/2011.02.004
Institute of Computer Science, Academy of Sciences CR, Pod Vodárenskou věží 2, Prague 182 00, Czech Republic
The basic inference function of mathematical statistics, the score function, is a vector function. The author has introduced the scalar score, a scalar inference function, which reflects main features of a continuous probability distribution and which is simple. Its simplicity makes it possible to introduce new relevant numerical characteristics of continuous distributions. The t-mean and score variance are descriptions of distributions without the drawbacks of the mean and variance, which may not exist even in cases of regular distributions. Their sample counterparts appear to be alternative descriptions of the observed data. The scalar score itself appears to be a new mathematical tool, which could be used in solving traditional statistical problems for models far from the normal one, skewed and heavy-tailed.
Statistics, inference function, data characteristics, point estimates, heavy tails.