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Asymptotic tail behavior of phase-type scale mixture distributions [article]

Leonardo Rojas-Nandayapa, Wangyue Xie
2017 arXiv   pre-print
We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable Y and a nonnegative but otherwise arbitrary  ...  Particular focus is given to phase-type scale mixture distributions where the scaling random variable S has discrete support --- such a class of distributions has been recently used in risk applications  ...  WX is supported by IPRS/APA scholarship at The University of Queensland.  ... 
arXiv:1502.01811v2 fatcat:gf4ybd3zcza2plaatq7swxnlfu

Calculation of ruin probabilities for a dense class of heavy tailed distributions

Mogens Bladt, Bo Friis Nielsen, Gennady Samorodnitsky
2014 Scandinavian Actuarial Journal  
In this paper we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions.  ...  It might be of interest to approximate a given heavy-tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide  ...  Phase-type distributions generalize mixtures and convolutions of exponential distributions, and are widely used in applied probability due to their tractability.  ... 
doi:10.1080/03461238.2013.865257 fatcat:su2f6wm63bfcpfa5qyxopuxphi

Fitting phase–type scale mixtures to heavy–tailed data and distributions

Mogens Bladt, Leonardo Rojas-Nandayapa
2018 Extremes  
We consider the fitting of heavy tailed data and distributions with a special attention to distributions with a non-standard shape in the "body" of the distribution.  ...  To this end we consider a dense class of heavy tailed distributions introduced in Bladt et al. (Scand. Actuar.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1007/s10687-017-0306-4 fatcat:ujik5qkecfchhhutytjhtt33d4

APR volume 44 issue 4 Cover and Front matter

2012 Advances in Applied Probability  
Tail behavior of randomly weighted sums 815 JINGCHEN LIU AND XUAN YANG.  ...  Asymptotic properties of the approximate inverse estimator for directional distributions General Applied Probability 977 JOAQUIN FONTBONA, HELENE GuERIN AND FLORENT MALRIEU.  ... 
doi:10.1017/s000186780000611x fatcat:xztjqaew5zb3zmy7lmlll7z2fy

Fitting phase--type scale mixtures to heavy--tailed data and distributions [article]

Mogens Bladt, Leonardo Rojas-Nandayapa
2017 arXiv   pre-print
To this end we consider a dense class of heavy tailed distributions introduced recently, employing an EM algorithm for the the maximum likelihood estimates of its parameters.  ...  We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution.  ...  INTRODUCTION In this paper we consider the maximum likelihood estimation for a dense class of nonnegative heavy-tailed tailed distributions, referred to as scale mixtures of phase-type distribuitions (  ... 
arXiv:1705.04357v1 fatcat:76ggkq2axjbella5v46osygg7m

On a Dirichlet Process Mixture Representation of Phase-Type Distributions

Daniel Ayala, Leonardo Jofré, Luis Gutiérrez, Ramsés H. Mena
2021 Bayesian Analysis  
An explicit representation of phase-type distributions as an infinite mixture of Erlang distributions is introduced.  ...  The representation unveils a novel and useful connection between a class of Bayesian nonparametric mixture models and phase-type distributions.  ...  With this in mind, we present an explicit representation of phase-type distributions as an infinite mixture of Erlang distributions.  ... 
doi:10.1214/21-ba1272 fatcat:e3xswxheiba53mx3ab67yfmvoq

Estimating the Parameters of Mixed Shifted Negative Binomial Distributions via an EM Algorithm

Mohsen Varmazyar, Raha Akhavan-Tabatabaei, Nasser Salmasi, Mohammad Modarres
2018 Scientia Iranica. International Journal of Science and Technology  
Discrete phase-type (DPH) distributions have one property that is not shared by continuous phase-type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable.  ...  in fitting fat-tailed distributions.  ...  Acknowledgment The authors thankfully acknowledge professor John Bowers for sharing information of Scottish NHS hospital from 1998 to 1999.  ... 
doi:10.24200/sci.2018.5130.1117 fatcat:nm6tfzgrxjh43gwe4qwtlaflk4

Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail

Stefan Wolfsheimer, Bernd Burghardt, Alexander K Hartmann
2007 Algorithms for Molecular Biology  
The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution.  ...  Finally, we study also the distribution of the sum statistics of the k best alignments.  ...  Score probability distributions for sum-statistics of the k-best scores (solid lines) for L = M = 200Figure 13 Score probability distributions for sum-statistics of the k-best scores (solid lines) for  ... 
doi:10.1186/1748-7188-2-9 pmid:17625018 pmcid:PMC1945026 fatcat:txmijf6atvh4fcpr2ygumj6p24

Approximation of Ruin Probabilities via Erlangized Scale Mixtures [article]

Oscar Peralta, Leonardo Rojas-Nandayapa, Wangyue Xie, Hui Yao
2017 arXiv   pre-print
Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size distribution is modelled as an Erlangized scale mixture.  ...  A distinctive feature of such a class is that it contains heavy-tailed distributions.  ...  WX is supported by IPRS/APA scholarship at The University of Queensland. HY is supported by APA scholarship at The University of Queensland.  ... 
arXiv:1705.09405v1 fatcat:hec26oymrvgynen5xbcgc5npay

Adaptive target detection in foliage-penetrating SAR images using alpha-stable models

A. Banerjee, P. Burlina, R. Chellappa
1999 IEEE Transactions on Image Processing  
A new target detection algorithm is proposed that 1) incorporates symmetric alpha-stable (SS) distributions for accurate clutter modeling, 2) constructs a two-dimensional (2-D) site model for deriving  ...  Results of our algorithm on real FOPEN images collected by the Army Research Laboratory are provided.  ...  Kapoor of ARL for the APD plot; and the reviewers, whose input has helped to improve this work.  ... 
doi:10.1109/83.806628 pmid:18267459 fatcat:y6e3g354jnbgtpgxo5s7dej3hy

A Novel Approach for Phase-Type Fitting with the EM Algorithm

A. Thummler, P. Buchholz, M. Telek
2006 IEEE Transactions on Dependable and Secure Computing  
In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely mixtures of Erlang distributions, to trace data.  ...  Hyper-Erlang Distributions and its Properties Hyper-Erlang Distributions We consider a mixture of M mutually independent Erlang distributions weighted with the (initial) probabilities α 1 ,...  ...  with r phases is defined as the sum of r independent identical exponentially distributed random variables.  ... 
doi:10.1109/tdsc.2006.27 fatcat:hfyjru2ljvh2fnfqzfyp2akmz4

Numerical Techniques in Lévy Fluctuation Theory

Naser M. Asghari, Peter Iseger, Michael Mandjes
2012 Methodology and Computing in Applied Probability  
We do so by approximating the Lévy process under consideration by another Lévy process for which the double transform Ee −αXτ(q) is known, with τ (q) an exponentially distributed random variable with mean  ...  1/q; then we use a fast and highly accurate Laplace inversion technique (of almost machine precision) to obtain the distribution ofX t .  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s)  ... 
doi:10.1007/s11009-012-9296-5 fatcat:4nwyf65venfjrizaisuwplayvq

The Multivariate Normal Inverse Gaussian Distribution: Em-Estimation And Analysis Of Synthetic Aperture Sonar Data

Roy Hansen, Alfred Hanssen, Tor Arne Oigård
2004 Zenodo  
Publication in the conference proceedings of EUSIPCO, Viena, Austria, 2004  ...  We fitted synthetic aperture sonar data to the MNIG distribution, and we found that the MNIG captured the inherent impulsiveness of these data with great accuracy.  ...  We believe that the MNIG distribution will prove to be useful for the modeling of impulsive signals, noise, and interference in multivariate sonar, radar, and communication systems.  ... 
doi:10.5281/zenodo.38451 fatcat:5ausioanzzbxvkoswxnhnby6sa

Page 3349 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
Tiit, Mixture of extremal distributions—a model alternative to the log- linear model (703-714); A. W. van der Vaart, Infinite-dimensional M-estimation (715-733); A. Yu.  ...  Linde, Small deviation probabilities of sums of independent random variables (59-74); Uwe Einmahl and David M.  ... 

Statistics of Co-Channel Interference in a Field of Poisson and Poisson-Poisson Clustered Interferers

Kapil Gulati, Brian L. Evans, Jeffrey G. Andrews, Keith R. Tinsley
2010 IEEE Transactions on Signal Processing  
Statistical modeling of interference is a useful tool to analyze outage probabilities in wireless networks and design interference-aware transceivers.  ...  distributions accurately model the statistical properties of the interference.  ...  The tail probability of the envelope random variable Y can then be expressed as otherwise. B.  ... 
doi:10.1109/tsp.2010.2072922 fatcat:q5jlit6lubfsdpdplhux6jxs4q
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