MULTIVARIATE DISTRIBUTIONS HAVING WEIBULL PROPERTIES

Random variables X1,..., Xn are said to have a joint distribution with Weibull minimums after arbitrary scaling if mini(aiXi) has a one dimensional Weibull distribution for arbitrary constants ai > 0, i = 1,..., n. Some properties of this class are demonstrated, and some examples are given which show the existence of a number of distributions belonging to the class. One of the properties is found to be useful for computing component reliability importance. The class is seen to contain an absolutely continuous Weibull distribution which can be generated from independent uniform and gamma distributions. © 1979.