  Different questions related with analysis of extreme values and outliers
arise frequently in practice. To exclude extremal observations and outliers is
not a good decision because they contain important information about the
observed distribution. The difficulties with their usage are usually related to
the estimation of the tail index in case it exists. There are many measures for
the center of the distribution, e.g. mean, mode, median. There are many
measures of the variance, asymmetry, and kurtosis, but there is no easy
characteristic for heavy-tailedness of the observed distribution. Here we
propose such a measure, give some examples and explore some of its properties.
This allows us to introduce a classification of the distributions, with respect
to their heavy-tailedness. The idea is to help and navigate practitioners for
accurate and easier work in the field of probability distributions.
  Using the properties of the defined characteristics some distribution
sensitive extremal index estimators are proposed and their properties are
partially investigated.
