Maximum Likelihood Estimation for Multi-Risk Model

In this paper we discuss a probabilistic model of failure due to competing causes of failure operating on a unit during its lifetime. Following Cox we term this the Multi-Risk Model. We impose some well-known parametric forms on the underlying distributions of the model and obtain maximum likelihood estimates for the parameters of the distributions. The asymptotic variance-covariance matrix of the estimates is derived. We give examples using the exponential and Weibull distributions. The theory is applied to data published by Mendenhall and Hader, who studied a Single-Risk Model.