When a word is used as an adverb then it is normally combined with a suffix like "-ly" or "-ian".
Like 'normal' becomes 'normally' and the previous sentence is an example of its use.
In statistics, common phrase have a construction like 'X is normally distributed', 'X is binomially distributed' or 'X is geometrically distributed'.
But less common are phrases like 'X is Poissonian distributed' or 'X is Bernoullian distributed'. (exception 'X is Gaussian distributed').
Why does the normal/Gaussian distribution get the use of an adverb-related suffix while this is not done as much with other distributions, especially with distributions that are named after a person?
Is the use of a suffix to make the root word an adverb correct?
The meaning 'X is normally distributed' is supposed to refer to 'X is distributed as a normal distribution' or 'X follows a normal distribution' (the normal distribution is the name of a particular type of probability distribution, it does not refer to 'normal' as in 'usual' or 'common'). There are also phrases like 'evenly distributed', but that relates more to the way that the distributing is done.
Some statistics about the use on the website stats.stackexchange.com is found with this query which allows counting the occurrences of sentence constructions like "is ... distributed".
With distributions that are named after a person the use of a suffix is less common.
with suffix | without suffix | |
---|---|---|
normally/normal | 610 | 19 |
geometrical/geometric | 4 | 1 |
binomially/binomial | 22 | 5 |
with suffix | without suffix | |
---|---|---|
Gaussian/Gauss | 10 | 0 |
Poissonian/Poisson | 0 | 33 |
Bernoullian/Bernoulli | 0 | 9 |
Hits on google.scholar
with suffix | without suffix | |
---|---|---|
Gaussian/Gauss | 16 600 | 169 |
Poissonian/Poisson | 92 | 15 900 |