2.52 ( ) For large m, the von Mises distribution (2.179) becomes sharply peaked around the mode 0. By defining = m1/2( 0)

2.52 ( ) For large m, the von Mises distribution (2.179) becomes sharply peaked around the mode θ0. By defining ξ = m1/2(θ − θ0) and making the Taylor expansion of the cosine function given by cos α = 1− α2 2

+ O(α4) (2.299)

show that as m→∞, the von Mises distribution tends to a Gaussian.