In many industrial situations, where systems must be monitored using data recorded throughout a historical period of observation, one cannot fully rely on sensor data, but often only has event data to work with. This, in particular, holds for legacy data, whose evaluation is of interest to...

This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized...

Despite rising concern over the biology of Sickle Cell Anaemia (SCA), no general modeling approach has considered the effects of the selective advantage of Haemoglobin S (HbS) over Haemoglobin (HbA). This paper develops a theoretical framework and demonstrates mathematically that mating between...

This paper studies the asymptotic behaviour of an affine stochastic functional differential equation modelling the evolution of the cumulative return of a risky security. In the model, the traders of the security determine their investment strategy by comparing short- and long-run moving...

In this paper, we study the interval availability Aw(t) of a repairable system through an integral equation. We proved initial monotonicity of the interval availability, and derived lower bounds to Aw(t) and average availability. The limit of the interval availability is also obtained. A...

We consider isotropic random motion where the direction alternations occur according to the renewal epochs of a Gamma distribution with shape parameter (n−2)/2, n=4,5,6,…, in higher dimensions. We formulate a general renewal-type equation for the characteristic function and we solve the...

This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized...

Weibull distributions play an important role in reliability studies and have many applications in engineering. It normally appears in the statistical scripts as having two parameters, making it easy to estimate its parameters. However, once you go beyond the two parameter distribution, things...