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To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes $(X_i,Y_i), i\ge 1$ and a claim counting random…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
Flooding results in 8 billion dollars of damage annually in the US and causes the most deaths of any weather related event. Due to climate change scientists expect more heavy precipitation events in the future. However, no current datasets…
The generalized extreme value (GEV) distribution is commonly employed to help estimate the likelihood of extreme events in many geophysical and other application areas. The recently proposed blended generalized extreme value (bGEV)…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
We consider forecasting functional time series of extreme values within a generalised extreme value distribution (GEV). The GEV distribution can be characterised using the three parameters (location, scale and shape). As a result, the…
The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values…
The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…
Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of…
Time series and extreme value analyses are two statistical approaches usually applied to study hydrological data. Classical techniques, such as ARIMA models (in the case of mean flow predictions), and parametric generalised extreme value…
Quantile and quantile effect functions are important tools for descriptive and causal analyses due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not…
Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk…
Sums of independent random variables form the basis of many fundamental theorems in probability theory and statistics, and therefore, are well understood. The related problem of characterizing products of independent random variables seems…