Hi,

In fable, I have generated forecasts using a SQRT transformation, and the (automatic) back-transformed SQUARED forecasts are:

```
fsteps mean sd
<chr> <dbl> <dbl>
1 f01_D 164415. 454.
2 f02_D 164560. 593.
3 f03_D 164715. 695.
4 f04_D 164854. 779.
5 f05_D 165001. 852.
6 f06_D 165147. 921.
```

these will be from a non-central-chi squared distribution: the SQUARE of a normal.

Simply, in ggplot2 or otherwise, I would like to plot EACH of the 6 non-central-chi squared PDF's, from the 6 forecasts on 2 plots:

(a) 6 PDF's superimposed

(b) 6 individual PDF's (on the same plot, using `library(patchwork)`

)

This I would like in 2 ways:

(1) Generating random variates: let's say 1000000 using `rchisq(n, df, ncp = ?)`

for EACH of the 6 forecasts.

(2) Analytically, using `dchisq(x, df, ncp = ?, log = FALSE)`

.

The parameters:

n = 1000000

df = 1: from theory, the square of the standard normal.

ncp = How do I calculate the non-centrality parameter ncp, given the **mean's and sd's**, for EACH of the 6 forecasts?

x = sequence from/to mean +/- 4*std say?

How do I plot the PDF's?

thanks,

Amarjit