  In the double rank analysis of research publications, the local rank position
of a country or institution publication is expressed as a function of the world
rank position. Excluding some highly or lowly cited publications, the double
rank plot fits well with a power law, which can be explained because citations
for local and world publications follow lognormal distributions. We report here
that the distribution of the number of country or institution publications in
world percentiles is a double rank distribution that can be fitted to a power
law. Only the data points in high percentiles deviate from it when the local
and world $\mu$ parameters of the lognormal distributions are very different.
The likelihood of publishing very highly cited papers can be calculated from
the power law that can be fitted either to the upper tail of the citation
distribution or to the percentile-based double rank distribution. The great
advantage of the latter method is that it has universal application, because it
is based on all publications and not just on highly cited publications.
Furthermore, this method extends the application of the well-established
percentile approach to very low percentiles where breakthroughs are reported
but paper counts cannot be performed.
