The Fisher distribution is central to palaeomagnetism but presents several problems when used
to characterize geomagnetic field directions as observed in sequences of volcanic rocks. First,
it introduces a shallowing effect when used to define the mean of any group of directional unit
vectors. This is problematic because it can suggest the presence of persistent non-axial dipole
components when none are present. More importantly, it fails to capture the observed ‘long
tail’ in distributions of both directions and associated virtual geomagnetic poles in terms of
angular distance from a central direction. To achieve a good fit to data, it therefore requires the
introduction of a second distribution (and therefore the estimation of additional parameters)
or the arbitrary removal of data. Here we present a new distribution to describe palaeomagnetic
directions and demonstrate that it overcomes both of these problems, generating robust
indicators of both the central direction (or pole position) and the spread of palaeomagnetic
data as defined by unit vectors. Starting from the assumption that poles (or directions) have
an expected colatitude, rather than a mean location, we derive the spherical exponential distribution.
We demonstrate that this new distribution provides a good fit to palaeomagnetic data
sets from seven large igneous provinces between 15 and 65 Ma and also those produced by
numerical dynamo models. We also use it to derive a new shape parameter which may be
used as a diagnostic tool for testing goodness of fit of models to data and use this to argue
for a shift in geomagnetic behaviour between 5 and 15 Ma. Furthermore, we point out that
this new statistic can be used to determine the most appropriate distribution to be used when
constructing confidence limits for poles
