Identification of parameters and the distribution of the maximum and the minimum

In problems of competing risks, where an individual may be subject to m causes of death and X(i) is the lifetime of an individual exposed to the ith cause, the X(i)s are not observable but only is their minimum, and inference is needed on the X(i) based on their minimum.;The same is the case with a m-component system, where the components are connected in series, and we are interested in inference on the lifetimes of the individual components. These examples motivate problems on parameter identification by the distribution of the minimum.;Similarly, the example of a m-component system where the components are connected in parallel motivates the corresponding maximum problem. In this thesis, these problems will be discussed in the context of Gamma, Weibull, Cauchy, Normal, and Poisson distributions.