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Register a new userStochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model
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Hamzeh Torabi
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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Let $X_{lambda_1}, ldots , X_{lambda_n}$ be independent non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i} X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1}, ldots, I_{p_n}$ are independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$. For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.
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Let $ X_{lambda_1},ldots,X_{lambda_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1},ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and $p_1,ldots,p_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$ and $p^*_1,ldots,p^*_n$. For illustration, we apply the results to some important models in actuary.
Let $ X_{lambda_1},ldots,X_{lambda_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1},ldots,I_{p_n}$ be independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. This paper considers comparing the smallest claim amounts from two sets of interdependent portfolios, in the sense of usual and likelihood ratio orders, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and $p_1,ldots,p_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$ and $p^*_1,ldots,p^*_n$. Also, we present some bounds for survival function of the smallest claim amount in a portfolio. To illustrate validity of the results, we serve some applicable models.
In this study, we focus on improving EUHFORIA (European Heliospheric Forecasting Information Asset), a recently developed 3D MHD space weather prediction tool. EUHFORIA consists of two parts, covering two spatial domains; the solar corona and the inner heliosphere. For the first part, the semi-empirical Wang-Sheeley-Arge (WSA) model is used by default, which employs the Potential Field Source Surface (PFSS) and Schatten Current Sheet (SCS) models to provide the necessary solar wind plasma and magnetic conditions above the solar surface, at 0.1 AU, that serve as boundary conditions for the inner heliospheric part. Herein, we present the first results of the implementation of an alternative coronal model in EUHFORIA, the so-called MULTI-VP model. We compared the output of the default coronal model with the output from MULTI-VP at the inner boundary of the heliospheric domain of EUHFORIA in order to understand differences between the two models, before they propagate to Earth. We also compared the performance of WSA+EUHFORIA-heliosphere and MULTI-VP+EUHFORIA-heliosphere against in situ observations at Earth. In the frame of this study, we considered two different high-speed stream cases, one during a period of low solar activity and one during a period of high solar activity. We also employed two different magnetograms, i.e., GONG and WSO. Our results show that the choice of both the coronal model and the magnetogram play an important role on the accuracy of the solar wind prediction. However, it is not clear which component plays the most important role for the modeled results obtained at Earth. A statistical analysis with an appropriate number of simulations is needed to confirm our findings.
Quantifying the uncertainty of wind energy potential from climate models is a very time-consuming task and requires a considerable amount of computational resources. A statistical model trained on a small set of runs can act as a stochastic approximation of the original climate model, and be used to assess the uncertainty considerably faster than by resorting to the original climate model for additional runs. While Gaussian models have been widely employed as means to approximate climate simulations, the Gaussianity assumption is not suitable for winds at policy-relevant time scales, i.e., sub-annual. We propose a trans-Gaussian model for monthly wind speed that relies on an autoregressive structure with Tukey $g$-and-$h$ transformation, a flexible new class that can separately model skewness and tail behavior. This temporal structure is integrated into a multi-step spectral framework that is able to account for global nonstationarities across land/ocean boundaries, as well as across mountain ranges. Inference can be achieved by balancing memory storage and distributed computation for a data set of 220 million points. Once fitted with as few as five runs, the statistical model can generate surrogates fast and efficiently on a simple laptop, and provide uncertainty assessments very close to those obtained from all the available climate simulations (forty) on a monthly scale.
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed.
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