DOC: Expand on the recommendations.

1 files changed, 22 insertions, 2 deletions

diff --git a/doc/source/reference/random/performance.rst b/doc/source/reference/random/performance.rst
index 3e5c20e3a..7121129d4 100644
--- a/doc/source/reference/random/performance.rst
+++ b/doc/source/reference/random/performance.rst
@@ -7,7 +7,27 @@ Performance
 
 Recommendation
 **************
-The recommended generator for single use is :class:`~PCG64`.
+The recommended generator for general use is :class:`~pcg64.PCG64`. It is
+statistically high quality, full-featured, and fast on most platforms, but
+somewhat slow when compiled for 32-bit processes.
+
+:class:`~philox.Philox` is fairly slow, but its statistical properties have
+very high quality, and it is easy to get assuredly-independent stream by using
+unique keys. If that is the style you wish to use for parallel streams, or you
+are porting from another system that uses that style, then
+:class:`~philox.Philox` is your choice.
+
+:class:`~sfc64.SFC64` is statistically high quality and very fast. However, it
+lacks jumpability. If you are not using that capability and want lots of speed,
+even on 32-bit processes, this is your choice.
+
+:class:`~mt19937.MT19937` `fails some statistical tests`_ and is not especially
+fast compared to modern PRNGs. For these reasons, we mostly do not recommend
+using it on its own, only through the legacy `~mtrand.RandomState` for
+reproducing old results. That said, it has a very long history as a default in
+many systems.
+
+.. _`fails some statistical tests`: https://www.iro.umontreal.ca/~lecuyer/myftp/papers/testu01.pdf
 
 Timings
 *******
@@ -44,7 +64,7 @@ The column labeled MT19973 is used the same 32-bit generator as
 
 
 The next table presents the performance in percentage relative to values
-generated by the legagy generator, `RandomState(MT19937())`. The overall
+generated by the legacy generator, `RandomState(MT19937())`. The overall
 performance was computed using a geometric mean.
 
 .. csv-table::