Minimum Kolmogorov–Smirnov test statistic parameter estimates

When a reliability analysis, survival analysis, or discrete-event simulation input modeling analysis is performed, it is typically the case that a modeler collects data associated with some system under consideration. Although this raw data provides an initial insight into the stochastic elements of the system, often it is desirable to construct a model of the system which is tractable for mathematical analysis, while remaining consistent with the data. Typically, some common parametric model is chosen, such as the exponential distribution, then a point estimation technique, such as maximum likelihood, is used to determine reasonable parameter estimates for the model. Finally, some goodness-of-fit test is performed to validate the model. However, this approach to modeling has two drawbacks. First, on the basis of experience and an initial examination of the raw data, the modeler chooses which model to use a priori, and then proceeds to choose reasonable parameters on the basis of data (for example λ̂ = 3.2, if an exponential (λ) model is chosen). The model is then assessed via a goodness-of-fit test. An obvious difficulty is that some other parametric model may have yielded an even better fit. A second and related problem has to do with the computation involved in finding parameter estimates. Analytical techniques for optimizing distribution parameters involve calculus. Likelihood functions for distributions with multiple parameters can be cumbersome to analyze. Differentiating them and solving for the estimators requires a symbolic language or a well designed algorithm to ensure correctness and efficiency. Further, as stated above, we know