In this thesis, we present the theory of generalised functions as a foundation of generalised stochastic processes. Afterwards, we introduced the generalised stochastic process, which serves as an abstraction of the conventional notion of stochastic processes. A particular case of generalised stochastic processes is the generalised random field, where a special case of these is of particular interest. Specifically, a so-called conformal model, called the De Wijs plus white noise process, is the centre of attention in the thesis. We present theory on parameter estimation for this process and seek to apply this to a particular dataset. To do this, we implement two different estimation method in the statistical programming language R. We then attempt to utilise these implemented functions on the so-called bcicov-dataset, which contains measurements of soil samples, from Barro Colorado Island in Panama.