The von Mises distribution is a continuous probability distribution
on the circle, and is used in applications of directional statistics such as grain orientation.
Hence a continuous probability distribution
function (pdf) becomes a discrete pdf that can be written:
The normal distribution is the continuous probability distribution
given by f(x)=1/[pi][e.
Although the Appendix discusses these commonly used examples, the body of this article focuses on the more realistic assumption of a continuous probability distribution
to describe the capital position of an insurer.
choose the most suitable continuous probability distribution
to use for a given scenario
The beta distribution is a family of continuous probability distributions
defined on the interval (0, 1) parameterized by two positive shape parameters, typically denoted by a and b.
The methodology proposed in this article utilizes an expert judgment model within a Bayesian framework for the more complex case of continuous probability distributions
, The most general form of Bayes' Theorem applies to discrete probability distributions, and relates the conditional and prior probabilities of two events using the following equation,