Von Mises Distribution - Limiting Behavior

Limiting Behavior

In the limit of large κ the distribution becomes a normal distribution

\lim_{\kappa\rightarrow\infty} f(x|\mu,\kappa)=\frac{\exp\left}{\sigma\sqrt{2\pi}}

where σ2 = 1/κ. In the limit of small κ it becomes a uniform distribution:

where the interval for the uniform distribution U(x) is the chosen interval of length 2π.

Read more about this topic:  Von Mises Distribution

Famous quotes containing the words limiting and/or behavior:

    “There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
    —Albert Einstein (1879–1955)

    “One cannot demand of a scholar that he show himself a scholar everywhere in society, but the whole tenor of his behavior must none the less betray the thinker, he must always be instructive, his way of judging a thing must even in the smallest matters be such that people can see what it will amount to when, quietly and self-collected, he puts this power to scholarly use.”
    —G.C. (Georg Christoph)