In this study the interval censoring case 2 model combined with the Cox model is considered. The event-time distribution function is modeled nonparametrically. Two algorithms are proposed to estimate the event-time distribution function together with the Cox coefficients. Kernel smoothing is applied to the non-parametric MLE of the event-time distribution resulting in the smoothed MLE (SMLE). A two-step method for choosing the smoothing bandwidth based on minimising the MSE is introduced. Given the SMLE, the precision of the MLE is tested using bootstrap simulations. New event-times are sampled from the SMLE which are then used to compute bootstrap estimates of the event-time distribution. This is done for multiple sample sizes to observe large sample behaviour. This study suggests that larger sample sizes lead to
better estimates. Monte Carlo simulations and the bootstrap simulations agree on the bandwidth and the large sample distribution of pointwise estimates of the event-time distribution.

[ not the actual abstract] In this thesis, the sandpile models distributions are analysed on the finite and infinite bethe lattice. To do so, the recursive property of the lattice is used.