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The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions. The concept is used in extreme value theory . Random variables that appear to exhibit no correlation can show tail dependence in extreme deviations.
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
The "68–95–99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal.
It is customary to transform data logarithmically to fit symmetrical distributions (like the normal and logistic) to data obeying a distribution that is positively skewed (i.e. skew to the right, with mean > mode, and with a right hand tail that is longer than the left hand tail), see lognormal distribution and the loglogistic distribution. A ...
Play the USA TODAY Daily Crossword Puzzle 'No Good Deed' trailer. Netflix dropped the trailer for "No Good Deed" On Nov. 14. We occasionally recommend interesting products and services. If you ...
Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation, mean absolute difference and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.
The most extreme case of a fat tail is given by a distribution whose tail decays like a power law. A variety of Cauchy distributions for various location and scale parameters. Cauchy distributions are examples of fat-tailed distributions. That is, if the complementary cumulative distribution of a random variable X can be expressed as [citation ...
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