# Histogram of noncentral chi-square variable shoots up when the number of histogram cells increases

Consider the random variable defined by: $$y=-8x+108$$ where $x$ follow a non-central chi-square distribution with 1 degree of freedom and a non-centrality parameter equal to 3.5, $x \sim \chi_{1}^{2}(3.5)$.

Why does the histogram shoots up when the number of cells increases?

See the graph below with 25 cells:

and with 1000 cells:

I got a very good answer from a related question here. I am however still a bit unclear of what is happening.

Here is the R code:

set.seed(101)
y<--8*rchisq(1000000, 1,3.5)+108
hist(y,freq=F,breaks=25,main="25 cells")
hist(y,freq=F,breaks=10000,,main="10000 cells")


Thanks!

• I suspect that if you ask yourself the inverse of this question--why does the spike in the second histogram disappear when the bins are broadened?--then the whole thing will become obvious. – whuber Jan 7 '15 at 17:39