Multivariate Reversed Hazard Rates and Inactivity Times of Systems

The family of the multivariate conditional hazard rate functions often reveals to be a convenient tool to describe the joint probability distribution of a vector of non-negative random variables (lifetimes) in the absolutely continuous case. Such a tool can have in particular an important role in the study of the behavior of the minima among inter-dependent lifetimes. In this paper we introduce the concept of reversed multivariate conditional hazard rate functions, which extends the one-dimensional notion of reversed hazard rate of a single non-negative random variable. Several basic properties of this concept are proven. In particular, we point out a related role in the study of the behavior of the maximum value among inter-dependent lifetimes. In different applied fields, and in particular in the reliability literature, a remarkable class of dependence models for vectors of lifetimes is related with the load-sharing condition, which can be defined in terms of the multivariate conditional hazard rate functions. In the paper we define the class of reversedload-sharing models, which can be seen as natural extensions to the multivariate case of the univariate inverse exponential distributions. We analyze basic properties of such a class of dependence models. In particular we show a result related to the study of the inactivity time of a coherent system when the joint distribution of the components’ lifetimes is a reversed load-sharing model.

Daily Labor Supply and Adaptive Reference Points

This paper provides field evidence on how reference points adjust, a degree of freedom in reference-dependence models. Examining this in the context of cabdrivers’ daily labor-supply behavior, we ask how the within-day timing of earnings affects decisions. Drivers work less in response to higher accumulated income, with a strong effect for recent earnings that gradually diminishes for earlier earnings. We estimate a structural model in which drivers work toward a reference point that adjusts to deviations from expected earnings with a lag. This dynamic view of reference dependence reconciles conflicting “neoclassical” and “behavioral” interpretations of evidence on daily labor-supply decisions. (JEL J22, J31, L94)

Knowledge Learning of Insurance Risks Using Dependence Models

Learning the customers’ experience and behavior creates competitive advantages for any company over its rivals. The insurance industry is an essential sector in any developed economy and a better understanding of customers’ risk profile is critical to decision making in all aspects of insurance operations. In this paper, we explore the idea of using copula-based dependence models to learn the hidden risk of policyholders in property insurance. Specifically, we build a novel copula model to accommodate the dependence over time and over space among spatially clustered property risks. To tackle the computational challenge caused by the discreteness feature of large-scale insurance data, we propose an efficient multilevel composite likelihood approach for parameter estimation. Provided that latent risk induces correlation, the proposed customer learning method offers improved predictive analytics by allowing insurers to borrow strength from related risks in predicting new risks and also helps reveal the relative importance of the multiple sources of unobserved heterogeneity in updating policyholders’ risk profile. In the empirical study, we examine the loss cost of a portfolio of entities insured by a government property insurance program in Wisconsin. We find both significant temporal and spatial association among property risks. However, their effects on the predictive distribution of loss cost are different for the new and renewal policyholders. The two sources of dependence are complements for the former and substitutes for the latter. These findings are shown to have substantial managerial implications in key insurance operations such as experience rating, capital allocation, and reinsurance arrangement.

One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems

The one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with accuracy and sharp bounds are provided. The longest increasing run statistics is related to the scan statistics and its distribution is studied. The moving average process is a particular case of block factor and the distribution of the associated scan statistics is approximated. Numerical results are presented.

Towards global stochastic flood modelling

<p>Hydraulic modelling at large spatial scales is a field of enquiry approaching a state of maturity, with the flood maps produced beginning to inform wide-area planning decisions, insurance pricing and emergency response. These maps, however, are typically ‘static’; that is, are a spatially homogeneous representation of a given probability flood. Actual floods vary in their extremity across space: if a given location is extreme, you may expect proximal locations to be similarly extreme and distal locations to be decreasingly extreme. Methods to account for this stochastically can, broadly speaking, be split into: (i) continuous simulation via a meteorological-hydrological-hydraulic model cascade and (ii) fitting statistical dependence models to samples of river gauges, generating a synthetic event set of streamflows and simulating the hydraulics from these. The former has the benefit of total spatial coverage, but the drawbacks of high computational cost and the low skill of large-scale hydrological models in simulating absolute river discharge. The latter enables higher-fidelity hydraulics in simulating the extremes only and with more accurately defined boundary conditions, yet it is only possible to execute (ii) in gauge-rich regions – excluding most of the planet.</p><p>In this work, we demonstrate that a hybrid approach of (i) & (ii) offers a promising path forward for stochastic flood modelling in gauge-poor areas. Inputting simulated streamflows from large-scale hydrological models to a conditional exceedance model which characterises the spatial dependence of discharge extremes produces a very different set of plausible flood events than when observed flows are used as boundary conditions. Yet, if the relative exceedance probability of simulated flows – internal to the hydrological model – are used in place of their absolute values (i.e. a return period instead of a value in m<sup>3</sup>s<sup>-1</sup>), the observation- and model-based dependence models produce similar events in terms of the spatial distribution of return periods. In the context of flood losses, when using Fathom-US CAT (a state-of-the-art large-scale stochastic flood loss model), the risk of an example portfolio is indistinguishable between the gauge- and model-driven framework given the uncertainty in vulnerability alone. This is providing the model-based event return period is matched up with a hydraulic model of the same return period, yet where the latter is characterised via a gauge-based approach.</p>

Dependence Models of Borehole Expansion on Explosive Charge in Spherical Cavity Blasting

In geotechnical practice, it is often necessary to improve the properties of soil and rock in which different structures are built. For this purpose, spherical cavity blasting can be applied to expand the borehole. Such expansion may incorporate various constructive elements such as anchors and thus stabilize the slope. The paper presents the method for determining the increased volume, expansion, and deepening of the borehole as a result of spherical cavity blasting. In addition, mathematical models describing the dependency of the borehole expansion on the amount of explosive charge are presented. The models are mutually compared with the Akaike information criterion.