A Flexible Extension to an Extreme Distribution

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

A study on the extreme value distribution of the minimum tensile strength of bolt

Taking M12.5 × 1.25 × 65-10.9 bolt as an example, this paper studies the extreme distribution of the minimum value of bolt tensile strength in order to evaluate the reliability and stability of bolt product quality and to verify the production process. Through data collection, parameter estimation, distribution test and extreme prediction, it is concluded that: 1) the distribution of the minimum value of bolt tensile strength conforms to Gumbel extreme distribution; 2) when the return period is 10000, the predicted minimum tensile strength is 1071.7 MPa ± 3.2 MPa, k = 2. It is higher than the minimum value of 1040 MPa required by ISO 898-1 standard.

Baseline Methods for Bayesian Inference in Gumbel Distribution

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.

Online Review Solicitations Reduce Extremity Bias in Online Review Distributions and Increase Their Representativeness

Representative online customer reviews are critical to the effective functioning of the Internet economy. In this study, I investigate the representativeness of online review distributions to examine how extremity bias and conformity impact it and explore whether online review solicitations alter representativeness. Past research on extreme distribution of online ratings commonly relied solely on observed public online ratings. One strength of the current paper is that I observe the private satisfaction ratings of customers regardless of whether they choose to write an online review or not. I show that both extremity bias and conformity exist in unsolicited online word-of-mouth (WOM) and introduce online review solicitations as a mechanism that can partially de-bias ratings. Solicitations increase all customers’ engagement in online WOM, but if solicited, those with moderate experiences increase their engagement more than those with extreme experiences. Consequently, although extremity bias still exists in solicited online WOM, solicitations significantly increase the representativeness of rating distributions. Surprisingly, the results demonstrate that without conformity, unsolicited online WOM would be even less representative of the original customer experiences. Furthermore, I document that both solicited and unsolicited reviews equally overstate the average customer experience (compared with average private ratings) despite stark differences in their rating distributions. Finally, I establish that solicitations for reviews on the company-owned website, on average, decrease the number of one-star reviews on a third-party review platform. This paper was accepted by Eric Anderson, marketing.

Probabilistic assessment of live load effects on continuous span bridges with regular and irregular configurations and its design implications

Studies on live load effects reported in recent literature are based on simple span bridges or on a limited number of continuous span bridges and regular configurations. In this study, an extensive probabilistic assessment of live load effects on continuous bridges is carried out for regular and irregular span configurations using weigh-in-motion data. Single vehicle passage is considered, and live load effects are compared with those from a live load model developed for simple spans from the same database. Truck models from Canada are also used for comparison purposes. Discussion of the fitting of extreme distribution is included, and an optimization scheme for the fitting is proposed. The most important finding of the study is that the use of live load models developed from simple spans or a limited number of continuous spans may not be suitable for designing continuous bridges, especially those with irregular configurations and short spans.

Extremes for high dimensional chaotic systems

<p>Extremes are related to high impact and serious hazard events and hence their study and prediction have been and continue to be highly relevant for all kind of applications in geoscience and beyond. Extreme value theory is promising to be able to predict them reliably and robustly. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to dynamical systems and has been related to properties of physical measure (statistical properties of the system), return and hitting times. We will review what one can say for highly dimensional perfectly chaotic systems.  We will concentrate on relations between the index of the extreme distribution and invariants of the underlying dynamical system which are stable, in the sense that they will continuously depend on changing parameters in the dynamics.  Furthermore, we explore whether there exists a response theory for extremes, that is, whether the change of extremes can be quantitatilvely expressed  in terms of changing parameters. </p><p> </p>

Firm Reputation, Innovation and Employee Startups

This article studies how a firm’s reputation for rewarding innovative employees affects innovation and startup creation. In any Pareto-efficient equilibrium of the repeated game, low-value innovations are developed in-house, while high-value innovations are developed in startups. When distributions of ideas are ordered by simple cases of first- or second-order stochastic dominance, the firm has a preference for an extreme distribution. The article also characterises the optimal relational contract and workers’ incentives to invest in innovation. The model’s predictions are consistent with a broad set of observed regularities regarding the creation of employee startups.