RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.

Modelling Insurance Losses with a New Family of Heavy-Tailed Distributions

The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues.In this article,we introduce a new class of heavy-tailed distributions useful for modeling data in financial sciences.A specific sub-model form of our suggested family,named as a new extended heavy-tailed Weibull distribution is examined in detail.Some basic characterizations,including quantile function and raw moments have been derived.The estimates of the unknown parameters of the new model are obtained via the maximum likelihood estimation method.To judge the performance of the maximum likelihood estimators,a simulation analysis is performed in detail.Furthermore,some important actuarial measures such as value at risk and tail value at risk are also computed.A simulation study based on these actuarial measures is conducted to exhibit empirically that the proposed model is heavy-tailed.The usefulness of the proposed family is illustrated by means of an application to a heavy-tailed insurance loss data set.The practical application shows that the proposed model is more flexible and efficient than the other six competing models including(i)the two-parameter models Weibull,Lomax and Burr-XII distributions(ii)the three-parameter distributions Marshall-Olkin Weibull and exponentiated Weibull distributions,and(iii)a well-known four-parameter Kumaraswamy Weibull distribution.

Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.

Large Deviations for Sums of Heavy-tailed Random Variables

This paper is a further investigation of large deviations for sums of random variables Sn=i=1∑n Xi and S（t）=i=1∑N（t）Xi,（t≥0）, where {X_n,n≥1） are independent identically distribution and non-negative random variables, and {N（t）,t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.

Median Unbiased Estimation of Bivariate Predictive Regression Models with Heavy-tailed or Heteroscedastic Errors

In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.

Persymmetric adaptive polarimetric detection of subspace range-spread targets in compound Gaussian sea clutter

This paper focuses on the adaptive detection of range and Doppler dual-spread targets in non-homogeneous and nonGaussian sea clutter.The sea clutter from two polarimetric channels is modeled as a compound-Gaussian model with different parameters,and the target is modeled as a subspace rangespread target model.The persymmetric structure is used to model the clutter covariance matrix,in order to reduce the reliance on secondary data of the designed detectors.Three adaptive polarimetric persymmetric detectors are designed based on the generalized likelihood ratio test(GLRT),Rao test,and Wald test.All the proposed detectors have constant falsealarm rate property with respect to the clutter texture,the speckle covariance matrix.Experimental results on simulated and measured data show that three adaptive detectors outperform the competitors in different clutter environments,and the proposed GLRT detector has the best detection performance under different parameters.

Kullback-Leibler Divergence Based ISAC Constellation and Beamforming Design in the Presence of Clutter

Integrated sensing and communication(ISAC)is regarded as a pivotal technology for 6G communication.In this paper,we employ Kullback-Leibler divergence(KLD)as the unified performance metric for ISAC systems and investigate constellation and beamforming design in the presence of clutters.In particular,the constellation design problem is solved via the successive convex approximation(SCA)technique,and the optimal beamforming in terms of sensing KLD is proven to be equivalent to maximizing the signal-to-interference-plus-noise ratio(SINR)of echo signals.Numerical results demonstrate the tradeoff between sensing and communication performance under different parameter setups.Additionally,the beampattern generated by the proposed algorithm achieves significant clutter suppression and higher SINR of echo signals compared with the conventional scheme.

Space-time clutter model for airborne bistatic radar with non-Gaussian statistics

To validate the potential space-time adaptive processing （STAP） algorithms for airborne bistatic radar clutter suppression under nonstationary and non-Gaussian clutter environments, a statistically non-Gaussian, space-time clutter model in varying bistatic geometrical scenarios is presented. The inclusive effects of the model contain the range dependency of bistatic clutter spectrum and clutter power variation in range-angle cells. To capture them, a new approach to coordinate system conversion is initiated into formulating bistatic geometrical model, and the bistatic non-Gaussian amplitude clutter representation method based on a compound model is introduced. The veracity of the geometrical model is validated by using the bistatic configuration parameters of multi-channel airborne radar measurement （MCARM） experiment. And simulation results manifest that the proposed model can accurately shape the space-time clutter spectrum tied up with specific airborne bistatic radar scenario and can characterize the heterogeneity of clutter amplitude distribution in practical clutter environments.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian-MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter（RFC） is a complicated nonlinear optimization problem.This paper deals with the RFC problem in a Bayesian framework.It uses the unbiased Markov Chain Monte Carlo（MCMC） sampling technique,which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework.In contrast to the global optimization algorithm,the Bayesian-MCMC can obtain not only the approximate solutions,but also the probability distributions of the solutions,that is,uncertainty analyses of solutions.The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar seaclutter data.Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter.The inversion algorithm is assessed（i） by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data;（ii） the one-dimensional（1D） and two-dimensional（2D） posterior probability distribution of solutions.

Modified GIT model for predicting wind-speed behavior of low-grazing-angle radar sea clutter

A modified GIT model for describing the variational trend of mean clutter reflectivity as a function of wind speed is proposed. It uses two slope adjustment factors and two critical wind-speed factors to define and adjust the increasing slope of reflectivity with respect to wind speed. In addition, it uses a constant factor to compensate the overall amplitude of clutter reflectivity. The performance of the modified GIT model has been verified on the basis of the L-band low-grazing-angle radar sea clutter data. The results are in good agreement with the experimental data, indicating that the model is more effective in predicting the wind-speed behavior of clutter reflectivity than the conventional GIT model, especially for lower and higher wind speeds. We believe that the proposed model can provide deeper insights into the relationship between radar sea clutter reflectivity and sea state conditions.

Study on Dim Target Detection and Discrimination from Sea Clutter

Dim target detection from sea clutter is one of the difficult topics in ocean remote sensing application. By aiming at the shortcoming of false alarms when using track before detect （TBD） based on dynamic programming, a new discrimination method called statistics of direction histogram （SDH） is proposed, which is based on different features of trajectories between the true target and false one. Moreover, a new series of discrimination schemes of SDH and Local Extreme Value method （LEV） are studied and applied to simulate the actually measured radar data. The results show that the given discrimination is effective to reduce false alarms during dim targets detection.

HF radar sea clutter rejection by nonlinear projections

In the background of signal detection for high frequency （I/F） radar, the sea clutter is quite significant and can mask some weak target signals. A new clutter rejection method named “nonlinear projection” is given to improve the SNR of the target. This approach is based on the recent observation that HF sea clutter may be modeled as a nonlinear deterministic dynamical system. After approximating the multidimensional reconstruction of the clutter by a low-dimensional attractor, projections onto this attractor can separate the clutter from other components. Real sea clutter, simulated target data and real target data are used to show that a nonlinear clutter rejection method is a promising technique to suppress sea clutter and enhances target detection.

Clutter suppression for hypersonic vehicle-borne radar with frequency diverse array

The seriously range-ambiguous clutter is one of the main problems in clutter suppression for hypersonic vehicle-borne forward-looking radar. An approach based on the frequency diverse array (FDA) technique is proposed to mitigate the range ambiguous clutter. The frequency increment is designed to distinguish the clutter at ambiguous ranges and suppress the clutter by using a subspace projection algorithm. On the platform with high altitude or limited array antennas, the proposed method performs better for its independence of the elevation degrees-of-freedom (DOF). Finally, simulation results verify the effectiveness of the proposed method.

Application of Fuzzy C-mean Cluster Algorithm on Clutter Tracking

This paper introduces a clutter tracking technique used forairborne PD radar. Combining the clutter feature of the airborne PDradar and characteristic of fuzzy C-means clustering algorithm, theauthors apply this algorithm to the clutter tracking, and present theflow chart. A method of defining the fuzzy membership function isalso proposed. The algorithm has been verified to be suc- cessful inseveral typical experiments.

Fractal-based weak target detection within sea clutter

The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis （DFA） has been used successfully to extract the time-domain Hurst exponent of sea-clutter series. Since the frequency of the sea clutter mainly concentrates around Doppler center so that we consider to extract frequency-do- main fractal characterization and then detect a weak target within sea clutter by using the difference of frequency-domain fractal characterization. The generalized detrended fluctuation analysis （GDFA） is more flexible than traditional DFA owing to its smoothing action for the clutters. In this paper, we apply the GDFA to evaluate the generalized Hurst exponent of sea-clutter series in the frequency domain. The difference of generalized Hurst exponents between different sea-clutter range bins would be used to determine whether the target exists. Moreover, some simulations with the real IPIX radar data have also been demonstrated in order to suooort this conclusion.

Inversion for atmosphere duct parameters using real radar sea clutter

This paper addresses the problem of estimating the lower atmospheric refractivity （M profile） under nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled using five parameters and the horizontal structure is modeled using five parameters. The refractivity model is implemented with and without a priori constraint on the duct strength as might be derived from soundings or numerical weather-prediction models. An electromagnetic propagation model maps the refractivity structure into a replica field. Replica fields are compared with the observed clutter using a squared-error objective function. A global search for the 10 environmental parameters is performed using genetic algorithms. The inversion algorithm is implemented on the basis of S-band radar sea-clutter data from Wallops Island, Virginia （SPANDAR）. Reference data are from range-dependent refractivity profiles obtained with a helicopter. The inversion is assessed （i） by comparing the propagation predicted from the radar-inferred refractivity profiles with that from the helicopter profiles, （ii） by comparing the refractivity parameters from the helicopter soundings with those estimated. This technique could provide near-real-time estimation of ducting effects.

A statistical distribution of quad-pol X-band sea clutter time series acquired at a grazing angle

Although the complex Wishart distribution has been widely used to analyze the statistic properties of quad-pol SAR spatial data, the applicability of this complex distribution to the time series of sea clutter is rarely discussed.The measured data of the quad-pol X-band marine radar demonstrate that the time series of the sea echoes are also satisfied the circular Gaussian distributions if the low intensity signals, which are mainly dominated by a radar noise, in the shadow regions of the large-scale waves are removed. On the basis of this fact, the probability density functions（PDFs） of the intensity as well as the phase, the real and the imaginary parts of the sea echoes obtained by the marine radar have been derived, and the theoretical models are all expressed in closed forms. In order to validate the theoretical results, the PDFs are compared with the experimental data collected by the Mc Master IPIX radar. And the comparisons show that the PDF models are in good agreement with the experimental data.

Optimal set integer programming algorithm for multiple maneuvering targets tracking in clutter

The aim of this paper is to solve the problems of multitarget tracking in clutter. Firstly, the data association of measurement-to-target is formulated as an integer programming problem. Through using the linear programming （LP） based branchand-bound method and adjusting the constraint conditions, an optimal set integer programming （OSIP） algorithm is then proposed for tracking multiple non-maneuvering targets in clutter. For the case of maneuvering targets, this paper introduces the OSIP algorithm into the filtering step of the interacting multiple model （IMM） algorithm resulting in the IMM based on OSIP algorithm. Extensive Monte Carlo simulations show that the presented algorithms can obtain superior estimations even in the case of high density noises.

Knowledge-based adaptive polarimetric detection in heterogeneous clutter

The detection performance and the constant false alarm rate behavior of the conventional adaptive detectors are severely degraded in heterogeneous clutter. This paper designs and analyses a knowledge-based （KB） adaptive polarimetric detector in het-erogeneous clutter. The proposed detection scheme is composed of a data selector using polarization knowledge and an adaptive polarization detector using training data. A polarization data selector based on the maximum likelihood estimation is proposed to remove outliers from the heterogeneous training data. This selector can remove outliers effectively, thus the training data is purified for estimating the clutter covariance matrix. Consequently, the performance of the adaptive detector is improved. We assess the performance of the KB adaptive polarimetric detector and the adaptive polarimetric detector without a data selector using simulated data and IPIX radar data. The results show that the KB adaptive polarization detector outperforms its non-KB counterparts.