Laleh Tafakori

Image denoising using generalised Cauchy filter

In many image processing analysis, it is important to significantly reduce the noise level. This study aims at introducing an efficient method for this purpose based on generalised Cauchy (GC) distribution. Therefore, some characteristics of GC distribution is considered. In particular, the characteristic function of a GC distribution is derived by using the theory of positive definite densities and utilising the density of a GC random variable as the characteristic function of a convolution of two generalised non-symmetric Linnik variables. Further, GC distribution is considered as a filter and in the proposed method for image noise reduction the optimal parameters of GC filter is defined by using the particle swarm optimisation. The proposed method is applied to different types of noisy images and the obtained results are compared with four state-of-the-art denoising algorithms. Experimental results confirm that their method could significantly reduce the noise effect.

An estimator of the stable tail dependence function based on the empirical beta copula

The replacement of indicator functions by integrated beta kernels in the definition of the empirical tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but superior finite-sample performance. The link of the new estimator with the empirical beta copula enables a simple but effective resampling scheme.

A new lifetime model with different types of failure rate

ABSTRACT A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.

A note on the Cauchy-type mixture distributions

ABSTRACT An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.

Forecasting Value at Risk for the Australian Electricity Returns: Spikes and Conditional Asymmetries in Return Innovations

This paper evaluates the accuracy of several hundred one-day-ahead value at risk (VaR) forecasts for predicting Australian electricity returns. We propose a class of observation-driven time series models referred to as asymmetric exponential generalised autoregressive score (AEGAS) models. The mechanism to update the parameters over time is provided by the scaled score of the likelihood function in the AEGAS model. Based on this new approach, the results provide a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models.The Australian energy markets is known as one of the most volatile and, when compared to some well-known models in the recent literature as benchmarks the fitting and forecasting results demonstrate the superior performance and considerable flexibility of proposed model for electricity markets.