# Is square-normal distribution another name for Chi-squared distribution?

This wiki page mentions square-normal distribution:

https://en.wikipedia.org/wiki/Probability_distribution_fitting

I google "square-normal distribution", it gives me Chi Square Distribution, but I cannot find any info that they're the same.

• The square of a standard normal (N(0,1)) random variable is $\chi^2_1$. The square of N(4,3) is not $\chi^2$ anything.
– Dave
Jan 14, 2020 at 1:30
• @Dave Terms like "square-normal" usually emulate the model of the "log-normal" distribution: in the latter case, to say $Y$ has a lognormal distribution mean the log of $Y$ is Normally distributed. Similarly, then, to say $Y$ has a "square-normal" distribution would ordinarily be understood as meaning the square of $Y$ has a Normal distribution. That indeed is what Wikipedia claims: "the normal distribution applied to the square of the data values." Unfortunately, there does not exist any such distribution. IMHO, that Wikipedia article is unusually poor and incomplete.
– whuber
Jan 14, 2020 at 13:58
• I 100% agree with the characterization of that WIkipedia article. Investigating the history it's almost entirely written by a single author (across a huge number of edits), and I don't see any point in time where it was worth an article on Wikipedia. Jan 20, 2020 at 0:25

Terms like "square-normal" usually emulate the model of the "log-normal" distribution: in the latter case, to say 𝑌 has a lognormal distribution mean the log of $$𝑌$$ is Normally distributed. Similarly, then, to say $$𝑌$$ has a "square-normal" distribution would ordinarily be understood as meaning the square of 𝑌 has a Normal distribution. That indeed is what Wikipedia claims: "the normal distribution applied to the square of the data values."