  Many objects studied in astronomy follow a power law distribution function,
for example the masses of stars or star clusters. A still used method by which
such data is analysed is to generate a histogram and fit a straight line to it.
The parameters obtained in this way can be severely biased, and the properties
of the underlying distribution function, such as its shape or a possible upper
limit, are difficult to extract. In this work we review techniques available in
the literature and present newly developed (effectively) bias-free estimators
for the exponent and the upper limit. The software packages are made available
as downloads. Furthermore we discuss various graphical representations of the
data and powerful goodness-of-fit tests to assess the validity of a power law
for describing the distribution of data. As an example, we apply the presented
methods to the data set of massive stars in R136 and the young star clusters in
the Large Magellanic Cloud. (abridged)
