Parameter Estimates and the Saved Prediction Formula

This is in JMP v15. Maybe in earlier versions of JMP the formula was expressed differently.

Since the link function is Log, the prediction must be exponentiated back to units of X.

Not a Poisson expert, but its a fun distribution because the center and scale parameters are equal. So when X is big it looks normal, and when X is close to 0 it looks log normal.

This is from the scripting index, super useful for understanding the behavior of the distribution at different levels of lambda

```
Names Default To Here( 1 );
lambda = 4;
New Window( "Example: Poisson Probability",
pdy = Graph Box(
Y Scale( 0, 0.20 ),
X Scale( -1, 40 ),
Pen Color( "red" ),
Pen Size( 2 );
For( k = 0, k <= 40, k++,
V Line(
k,
0,
Poisson Probability( lambda, k )
)
);
Text(
{30, 0.18},
"\!U03BB=",
Round( lambda, 2 )
);
),
H List Box(
Slider Box( 0, 40, lambda, pdy << reshow ),
Text Box( " \!U03BB" )
)
);
```

JMP Systems Engineer, Pharm and BioPharm Sciences