Nineteen Atlantic tropical storms 3 consecutive years: a very rare event

How rare are 3 consecutive top-five hurricane seasons for named storms?
It is tremendously rare to get three consecutive top-five years in a database with a 162-year record. This would occur randomly just once every 34,000 years--assuming the database were unbiased, the climate were not changing, and a multi-year climate pattern favorable for active seasons were not present. However the database IS biased, the climate IS changing, and we have been in an active hurricane period that began in 1995. So, which of these factors may be responsible for recording three consecutive years with nineteen named storms? It is well-known that prior to the arrival of geostationary satellites in December 1966 and aircraft hurricane reconnaissance in 1945 that tropical storms in the Atlantic were under-counted. Landsea et al. (2004) theorized that we missed up to six named storms per year between 1851 - 1885, and up to four between 1886 - 1910. Landsea (2007) estimated the under-count to be 3.2 named storms per year between 1900 - 1965, and 1.0 per year between 1966 - 2002. Other studies have argued for lower under-counts. So, if we assume the highest under-counts estimated by Landsea et al. (2004) and Landsea (2007), here would be the top ten busiest Atlantic hurricane seasons since 1851:

2005: 28
1887: 25
1933: 23
1995: 20
2012, 2011, 2010, 1969, 1936: 19

http://www.wunderground.com/blog/JeffMasters/article.html?entrynum=2301