Ever since the introduction by Rao in 1945 of the Fisher
information metric on a family of probability distributions there
has been interest among statisticians in the application of
differential geometry to statistics. This interest has increased
rapidly in the last couple of decades with the work of a large
number of researchers. Until now an impediment to the spread of
these ideas into the wider community of statisticians is the lack
of a suitable text introducing the modern co-ordinate free approach
to differential geometry in a manner accessible to statisticians.
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