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 whichsuch 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 propertiesof the underlying distribution function, such as its shape or a possible upperlimit, are difficult to extract. In this work we review techniques available inthe literature and present newly developed (effectively) bias-free estimatorsfor the exponent and the upper limit. The software packages are made availableas downloads. Furthermore we discuss various graphical representations of thedata and powerful goodness-of-fit tests to assess the validity of a power lawfor describing the distribution of data. As an example, we apply the presentedmethods to the data set of massive stars in R136 and the young star clusters inthe Large Magellanic Cloud. (abridged)
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