Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing

Interval bounds for the optimal burn-in times for concave or convex reward functions

An interesting problem in reliability is to determine the optimal burn-in time. In a previous work, the authors studied the solution of such a problem under a particular cost structure. It has been shown there that a key role in the problem is played by a function $\rho$, representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when $\rho$ is linear. In this paper, we explore further the linear case and use its solutions as a benchmark for determining the locally optimal times when the function $\rho$ is not linear or under a different cost structure

Interactions between ageing and risk properties in the analysis of burn-in problems

Several relevant problems in reliability can be looked at as problems of risk management and of decisions in the face of uncertainty. However, in this frame, the so-called burn-in problem can be seen as a problem of risk taking par excellence. In this paper, we in particular point out some aspects concerning interactions between the probabilistic model for lifetimes and considerations of an economic kind. As one of the features of our work, we hinge on some unexplored connections between ageing properties of a one-dimensional survival function Formula and risk-aversion-type properties of the function u(t) = bG(t), b > 0, when the latter is seen as a utility function

Diffusive behavior and the modeling of characteristic times in limit order executions

We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays asymptotically as a power law, but that of FPT has significantly fatter tails than that of TTF. Thus a simple first passage time model cannot account for the observed TTF of limit orders. We propose that the origin of this difference is the presence of cancellations. We outline a simple model, which assumes that prices are characterized by the empirically observed distribution of the first passage time and orders are canceled randomly with lifetimes that are asymptotically power law distributed with an exponent lambda_LT. In spite of the simplifying assumptions of the model, the inclusion of cancellations is enough to account for the above observations and enables one to estimate characteristics of the cancellation strategies from empirical data.Comment: 17 pages, 9 figures, 6 tables, to appear in Quantitative Financ

A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model

Addressing failure rate uncertainties of marine energy converters

publication-status: Publishedtypes: ArticleThe interest in marine renewable energy is strong, but has not led to significant commercial-scale investment and deployment, yet. To attract investors and promote the development of a marine renewable industry a clear concept of project risk is paramount, in particular issues relating to device reliability are critical. In the public domain, reliability information is often scarce or inappropriate at this early stage of development, as little operational experience has been gained. Thus, reliability estimates are fraught with large uncertainties. This paper explores sources and magnitudes of failure rate uncertainty and demonstrates the effect on reliability estimates for a notional marine energy converter. If generic failure rate data forms the basis of a reliability assessment, reliability estimates are not robust and may significantly over- or underestimate system reliability. The Bayesian statistical framework provides a method to overcome this issue. Generic data can be updated with more specific information that could not be statistically incorporated otherwise. It is proposed that adopting such an approach at an early stage in an iterative process will lead to an improved rate of certainty