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The exponential distribution plays a key role in the practical application of reliability theory, survival analysis, engineering and queuing theory. These applications often rely on the underlying assumption that the observed data originate from an exponential distribution. In this paper, two new tests for exponentiality are proposed, which are based on a conditional second moment characterisation. The proposed tests are compared to various established tests for exponentiality by means of a simulation study where it is found that the new tests perform favourably relative to the existing tests. The tests are also applied to real-world data sets with independent and identically distributed data as well as to simulated data from a Cox proportional hazards model, to determine whether the residuals obtained from the fitted model follow a standard exponential distribution.

Survival analysis has become a popular technique to more accurately model the probability of default in the credit risk environment with the ultimate goal of finding the optimal price for credit. In this paper we present an overview of some of the basic concepts of survival analysis. The focus is specifically on the Cox Proportional Hazards (CPH) model and the mixture cure model, which is a general alternative to the CPH model. A detailed algorithm that can be used to simulate survival times (default times) from a mixture cure model is provided. A parametric CPH and mixture cure model are fitted to a simulated data set and the benefits of fitting the latter model are illustrated.