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A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
In this paper, some new results on the distribution of the generalized singular value decomposition (GSVD) are presented.
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
Grand Unified Theories (GUTs) are one of the most interesting high-energy completions of the Standard Model, because they provide a rich, powerful and elegant group-theoretical framework able to resolve a variety of problems remaining in…
The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness…
We propose the Generalized Probabilistic U-Net, which extends the Probabilistic U-Net by allowing more general forms of the Gaussian distribution as the latent space distribution that can better approximate the uncertainty in the reference…
Exact distribution of the moment estimator of shape parameter for the gamma distribution for small samples is derived. Order preserving properties of this estimator are presented.
The main result of the paper is the following. Let a non-degenerate distribution have finite moments $\mu_k$ of all orders $k=0,1,2,\ldots$. Then the sequence $\{\mu_k/k!, \; k=0,1,2,\ldots\}$ either contains infinitely many different terms…
The Median Based Unit Weibull is a new 2 parameter unit Weibull distribution defined on the unit interval (0,1). Estimation of the parameters using MLE encountered some problems like large variance. Using generalized method of moments…
A new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied. The model has as special cases new four- and three-parameter…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
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…
A slightly revised version of notes distributed during a short course on GPTs, given at the Perimeter Institute for Theoretical Physics in March and April of 2024.
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which…
We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n-1 from the uniform distribution U(0,1), for each n. A new…
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an…