This thesis aims to improve Coolblue's direct demand estimation model for substitutable products. Their current model consists of three sub-models which all provide their direct demand estimations. For every product, the direct demand is taken from one of the sub-models based on their performance in estimating the sales. The sub-models are the mean, linear and expectation-maximisation (EM) model. The linear model gives the most accurate expectations, whereas the mean model scores the lowest. Therefore, we have improved the mean model's estimations by creating a new estimator. Furthermore, we have investigated if an out-of-stock (OOS) period influences the sales and, therefore, the direct demand estimations. From this investigation, we conclude that for a part of the products, the sales are affected by OOS periods. However, these results are dependent on how they are investigated. Moreover, the OOS periods' influences are as likely to be positive as negative on the sales. Therefore it is challenging to react to these influences.

The clustering of events can have a large impact on society. The extremal index $\theta$ tells how much extreme events cluster. We will compare different types of estimators in this project. First, we review the extremes of different sequences which have different values of $\theta$. We have found significant differences between the extremes. Then, 2 different types of estimators are introduced which both use different ways to divide the data, using disjoint blocks and using sliding blocks. The optimal block lengths are simulated for all those estimators. Using those block lengths, $\theta$ is simulated with all the estimators. From the simulations we conclude that the estimators using sliding blocks perform better. The best-performed estimator that we found from the simulations is used to estimate $\theta$ on data from the KNMI, comparing wind gusts and precipitation at weather stations De Bilt and Vlissingen.