Coxian and Related Distributions
Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot · Wiley series in probability and statistics · 2013
This chapter discusses two fairly broad classes of models that have been used in applications involving loss models. Both are subclasses of the class of Coxian distributions, which we define. The class of combinations of exponentials is an important class of distributions as it is dense in the set of probability distributions on [0,∞), implying that any such probability distribution may be approximated by a combination of exponentials. Interestingly, the terminology “logbeta” is also due to Dufresne and is more appropriate than the use of the term “lognormal” in that the log (not the exponential) of a lognormal random variable is normally distributed. Controlled Vocabulary Terms autoregressive models; exponential distribution; polynomial function models; probability