Pinning the tail on the distribution: A multivariate extension to the generalised Pareto distribution

2011 ◽  
Author(s):  
David A. Clifton ◽  
Samuel Hugueny ◽  
Lionel Tarassenko
Keyword(s):  
Pareto Distribution ◽  
Multivariate Extension ◽  
Generalised Pareto Distribution

scholarly journals Generalised Smooth Tests for the Generalised Pareto Distribution

2011 ◽  
Vol 5 (4) ◽  
pp. 737-750 ◽  
Author(s):  
B. De Boeck ◽  
O. Thas ◽  
J. C. W. Rayner ◽  
D. J. Best
Keyword(s):  
Pareto Distribution ◽  
Smooth Tests ◽  
Generalised Pareto Distribution

scholarly journals From the General Affine Transform Family to a Pareto Type IV Model

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Analytical Form ◽  
Common Solution ◽  
Affine Transform ◽  
Type Iv ◽  
Generalised Pareto Distribution ◽  
Iv Model ◽  
General Affine ◽  
Pathological Situation

The analytical form of general affine transform families with given maximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type IV model.

Modeling of Motor Vehicle Claims Using Extreme Value Methodology and Monte Carlo Stimulation: A Comparative Study

2008 ◽  
Vol 4 (4) ◽  
pp. 96-103
Author(s):  
S. Chandrasekhar
Keyword(s):  
Monte Carlo ◽  
Pareto Distribution ◽  
Motor Vehicle ◽  
Claim Data ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Claim Amount ◽  
Insurance Claims ◽  
Value Analysis ◽  
Generalised Pareto Distribution

Motor Vehicle Insurance claims form a substantial component of Non life insurance claims and it is also growing with increasing number of vehicles on roads. It is also desirable to have an idea of what will be the likely claim amount for the coming future (Monthly, Quarterly, Yearly) based on past claim data. If one looks at the claim amount one can make out that there will be few large claims compared to large number of average and below average claims. Thus the distributions of claims do not follow a Symmetric pattern which makes it difficult using normal Statistical analysis. The methodology followed to analyze such data is known as Extreme value Analysis. Extreme value analysis is a general name which covers (i) Generalised Extreme Value (GEV) (ii) Generalised Pareto Distribution (GPD). Basically these techniques can deal with non symmetric shape of the distribution which is close to reality. Normally one fits a generalised Extreme Value distribution (GEV)/Generalised Pareto Distribution (GPD) and using parameters of fitted distribution future, forecast of likely losses can be predicted. Second method of analyzing such data is using methodology of simulation. Here we fit a Poisson distribution for arrival of claims and weibull/pareto/Lognormal for claim amount. Using Monte Carlo Simulation one combines both the distributions for future prediction of claim amount. This paper shows a comparison of the above techniques on motor vehicle claims data.

scholarly journals Associating Stochastic Modelling of Flow Sequences With Climatic Trends

2021 ◽  
Author(s):  
Sandhya Patidar ◽  
Eleanor Tanner ◽  
Bankaru-Swamy Soundharajan ◽  
Bhaskar Sen Gupta
Keyword(s):  
Pareto Distribution ◽  
Southern Oscillation ◽  
Extreme Value Distribution ◽  
Stochastic Modelling ◽  
Life Forms ◽  
Enso Events ◽  
Climatic Trends ◽  
Modelling Framework ◽  
Highly Sensitive ◽  
Generalised Pareto Distribution

Water is essential to all life-forms including various ecological, geological, hydrological, and climatic processes/activities. With changing climate, associated El Nino/Southern Oscillation (ENSO) events appear to stimulate highly uncertain patterns of precipitation (P) and evapotranspiration (EV) processes across the globe. Changes in P and EV patterns are highly sensitive to temperature variation and thus also affecting natural streamflow processes. This paper presents a novel suite of stochastic modelling approaches for associating streamflow sequences with climatic trends. The present work is built upon a stochastic modelling framework HMM_GP that integrates a Hidden Markov Model with a Generalised Pareto distribution for simulating synthetic flow sequences. The GP distribution within HMM_GP model is aimed to improve the model's efficiency in effectively simulating extreme events. This paper further investigated the potentials of Generalised Extreme Value Distribution (EVD) coupled with an HMM model within a regression-based scheme for associating impacts of precipitation and evapotranspiration processes on streamflow. The statistical characteristic of the pioneering modelling schematic has been thoroughly assessed for their suitability to generate/predict synthetic river flows sequences for a set of future climatic projections. The new modelling schematic can be adapted for a range of applications in the area of hydrology, agriculture and climate change.

scholarly journals Uncertainty in calibrating generalised Pareto distribution to rainfall extremes in Lake Victoria basin

2014 ◽  
Vol 46 (3) ◽  
pp. 356-376 ◽  
Author(s):  
Charles Onyutha ◽  
Patrick Willems
Keyword(s):  
Parameter Estimation ◽  
Pareto Distribution ◽  
Lake Victoria ◽  
Estimation Method ◽  
Eastern Africa ◽  
Rainfall Time Series ◽  
Lake Victoria Basin ◽  
Parameter Estimation Method ◽  
Rainfall Extremes ◽  
Generalised Pareto Distribution

Uncertainty in the calibration of the generalised Pareto distribution (GPD) to rainfall extremes is assessed based on observed and large number of global climate model rainfall time series for nine locations in the Lake Victoria basin (LVB) in Eastern Africa. The class of the GPD suitable for capturing the tail behaviour of the distribution and extreme quantiles is investigated. The best parameter estimation method is selected following comparison of the method of moments, maximum likelihood, L-moments, and weighted linear regression in quantile plots (WLR) to quantify uncertainty in the extreme intensity quantiles by employing the Jackknife method and nonparametric percentile bootstrapping in a combined way. The normal tailed GPD was found suitable. Although the performance of each parameter estimation method was acceptable in a number of evaluation criteria, generally the WLR technique appears to be more robust than others. The difference between upper and lower limits of the 95% confidence intervals expressed as a percentage of the empirical 10-year rainfall intensity quantile ranges from 9.25 up to 59.66%. The assessed uncertainty will be useful in support of risk based planning, design and operation of water engineering and water management applications related to floods in the LVB.

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