DISTRIBUTION of LINEAR FRACTAL INTERPOLATION FUNCTION for RANDOM DATASET with STABLE NOISE

In this paper, we derive the probability distribution of linear fractal interpolation function (FIF) for a random dataset on R2, where randomness in the data is induced, using α-stable noise, in the second coordinate. In particular, we show that the distribution of linear FIF, at any point (on the first coordinate), is also stable, but with different parameters which can be estimated. Finally, we also provide statistical validity of our results.