Topic
K-distribution
About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.
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TL;DR: In this article, the authors have fitted two heavy tailed distributions viz the Weibull distribution and the Burr XII distribution to a set of Motor insurance claim data and used them to obtain an approximation to the probability of ultimate ruin through Pollaczek-Khinchin formula by Monte Carlo simulation.
Abstract: In this paper, we have fitted two heavy tailed distributions viz the Weibull distribution and the Burr XII distribution to a set of Motor insurance claim data. As it is known, the probability of ruin is obtained as a solution to an integro differential equation, general solution of which leads to what is known as the Pollaczek-Khinchin Formula for the probability of ultimate ruin. In case, the claim severity is distributed as the above two mentioned distributions, and Pollaczek-Khinchin formula cannot be used to evaluate the probability of ruin through inversion of their Laplace transform since the Laplace Transforms themselves don’t have closed form expression. However, an approximation to the probability of ultimate ruin in such cases can be obtained by the Pollaczek-Khinchin formula through simulation and one crucial step in this simulation is to simulate from the corresponding Equilibrium distribution of the claim severity distribution. The paper lays down methodologies to simulate from the Equilibrium distribution of Burr XII distribution and Weibull distribution and has used them to obtain an approximation to the probability of ultimate ruin through Pollaczek-Khinchin formula by Monte Carlo simulation. An attempt has also been made to obtain numerical values to the probability function for the number of claims until ruin in case of zero initial surplus under these claim severity distributions and this in turn necessitates the computation of the convolutions of these distributions. The paper makes a preliminary effort to address this issue. All the computations are done under the assumption of the Classical Risk Model.
2 citations
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TL;DR: Probability distributions associated with several ‘iff’ ply operators are discussed and these exact distributions are compared with relevant normal approximants.
2 citations
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01 Sep 2009TL;DR: In this paper, an improved parameter estimation algorithm was developed to estimate parameters of the homodyned K distribution, i.e., the effective number of scatterers per resolution cell and k (ratio of coherent to diffuse energy) parameters.
Abstract: The amplitude distribution of the envelope of backscattered ultrasound depends on tissue microstructure. By fitting measured envelope data to a model, parameters can be estimated to describe properties of underlying tissue. The homodyned K distribution is a general model that encompasses the scattering situations modeled by the Rice, Rayleigh, and K distributions. However, parameter estimation for the homodyned K distribution is not straightforward because the model is analytically complex. Furthermore, effects of frequency-dependent attenuation on parameter estimates need to be assessed. An improved parameter estimation algorithm was developed to quickly and accurately estimate parameters of the homodyned K distribution, i.e., the μ (effective number of scatterers per resolution cell) and k (ratio of coherent to diffuse energy) parameters. Parameter estimates were found by fitting estimates of SNR, skewness, and kurtosis of fractional-order moments of the envelope with theoretical values predicted by the homodyned K distribution. The effects of frequency dependent attenuation were approximated by assuming a Gaussian pulse to determine the shift in center frequency of the pulse and hence change in volume of the resolution cell. Computational phantoms were created with varying attenuation coefficients and scanned using a simulated f/4 transducer with a center frequency of 10 MHz. An average of two scatterers per resolution cell (based on the phantoms with no attenuation) was used. The new estimation algorithm was tested and compared with an existing algorithm (based on the even moments of the homodyned K distribution). The new estimation algorithm was found to produce estimates with lower bias and variance. For example, for μ = 2 and k ranging from 0 to 2 in steps of 0.1, the average variance in the μ parameter estimates was 0.067 for the new algorithm and 0.42 for existing algorithm. For the k parameter estimates, the average variance was 0.0069 for the new algorithm and 0.048 for the old algorithm. In the simulations with no attenuation, the μ parameter estimate was 2.53±0.18. In the phantoms with a linear attenuation coefficient of 0.5 dB·MHz−1·cm−1, the estimate was 4.64±0.54. This compared well with the predicted μ value of 4.98.
2 citations
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13 May 2012TL;DR: This paper generalizes probability-possibility transformations to two-dimensional distributions with a particular care to the maximum specificity principle, so that joint probability distributions can be suitably transformed into maximally specific joint possibility distributions.
Abstract: In the recent years the possibility theory has been investigated by many Authors in the field of mathematics and engineering. A possibility distribution is, from the mathematical point of view, a generalization of a probability distribution, since it can represent a family of probability distributions. Given a probability distribution, different probability-possibility transformations have been defined, which transform the probability distribution into different possibility distributions. Probability-possibility transformations are useful in any problem where statistical data must be dealt within the possibility theory, together with other heterogeneous uncertain and imprecise data. This paper generalizes these transformations to two-dimensional distributions with a particular care to the maximum specificity principle, so that joint probability distributions can be suitably transformed into maximally specific joint possibility distributions.
2 citations