=+12. The von Mises density e cos(y) 2I0() , 0 is a concentration parameter, and the

=+12. The von Mises density eκ cos(y−α)

2πI0(κ) , −π 0 is a concentration parameter, and the modified Bessel function I0(κ) is the normalizing constant I0(κ) = 1 2π

 π

−π

eκ cos ydy.

Verify that Laplace’s method yields I0(κ) 

eκ

√2πκ

as κ → ∞. For large κ it is clear that the von Mises distribution is approximately normal.

320 12. Asymptotic Methods