Composite Pareto Distributions for Modelling Household Income Distribution in Malaysia

Composite Pareto distributions are flexible as the models allow for data to be described by two distributions: a Pareto distribution for the data above a threshold value and another separate distribution for data below the threshold value. It is noted in some previous literatures that the Paretian tail behaviour can be observed in the distribution of Malaysian household income. In this paper, the composite Pareto models are fitted to the Malaysian household income data of several years. These fitted composite Pareto models are then compared to several univariate models for describing income distribution using pseudo-likelihood based AIC, BIC and Kolmogorov-Smirnov goodness-of-fit test. It is found that the income distributions in Malaysia can be best described by the lognormal-Pareto (II) model as compared to other candidate models.

The dust tail gap of C/2014 Q1 (PanSTARRS)

<p>A dust tail ‘gap’ was discovered in amateur images of the dust tail of C/2014 Q1 (PanSTARRS), which appeared around the comet’s most recent perihelion on 6<sup>th</sup> July 2015. This gap presented itself as a wedge-shaped region devoid of dust, with the comet’s dust tail appearing to be normal on either side of this dark zone.</p> <p>The results of the C/2014 Q1 study, employing Finson-Probstein modelling of the dust tail, show that none of the dust lay along the comet’s orbital path, confirming that both sections of dust were part of the dust tail and not a typical separation between dust tail and dust trail. A gap, devoid of dust, separates these two sections. The edges of this gap are bounded fairly accurately by lines of constant dust ejection time, corresponding to dust that should have been ejected between 6<sup>th</sup> July and 12<sup>th</sup> July. This suggests that cometary activity between these two dates was drastically reduced, although the cause of this is still unknown. The gap was visible throughout July and August 2015, and its shape and structure remained constant in the context of expected dust tail behaviour.  </p> <p>The limited dataset for C/2014 Q1 meant that the formation mechanism of this gap could not be fully investigated.  However, a subsequent survey of amateur and professional comet images revealed the presence of similar gaps in the dust tails of several other comets. Analysis of these comets show many similarities with the results of the C/2014 Q1 study, including that these dust gaps observed all form during the comets’ perihelia. We present the results of individual analyses and cross-comparison of these comets, and summarize what we believe are the most likely scenarios for the formation of these perplexing features. </p>

Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel

This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski’s coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel K K which can be written as K = 2 + ε W K=2+\varepsilon W . The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on W W , we will show that for sufficiently small ε \varepsilon there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile. Establishing uniqueness of self-similar profiles for Smoluchowski’s coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel.

Means and Extremes: Evaluation of a CMIP6 Multi-Model Ensemble in Reproducing Historical Climate Characteristics across Alberta, Canada

This study evaluates General Circulation Models (GCMs) participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) for their ability in simulating historical means and extremes of daily precipitation (P), and daily maximum (Tmax), and minimum temperature (Tmin). Models are evaluated against hybrid observations at 2255 sub-basins across Alberta, Canada using established statistical metrics for the 1983–2014 period. Three extreme indices including consecutive wet days (CWD), summer days (SD), and warm nights (WN) are defined based on the peak over the threshold approach and characterized by duration and frequency. The tail behaviour of extremes is evaluated using the Generalized Pareto Distribution. Regional evaluations are also conducted for four climate sub-regions across the study area. For both mean annual precipitation and mean annual daily temperature, most GCMs more accurately reproduce the observations in northern Alberta and follow a gradient toward the south having the poorest representation in the western mountainous area. Model simulations show statistically better performance in reproducing mean annual daily Tmax than Tmin, and in reproducing annual mean duration compared to the frequency of extreme indices across the province. The Kernel density curves of duration and frequency as simulated by GCMs show closer agreement to that of observations in the case of CWD. However, it is slightly (completely) overestimated (underestimated) by GCMs for warm nights (summer days). The tail behaviour of extremes indicates that GCMs may not incorporate some local processes such as the convective parameterization scheme in the simulation of daily precipitation. Model performances in each of the four sub-regions are quite similar to their performances at the provincial scale. Bias-corrected and downscaled GCM simulations using a hybrid approach show that the downscaled GCM simulations better represent the means and extremes of P characteristics compared to Tmax and Tmin. There is no clear indication of an improved tail behaviour of GPD based on downscaled simulations.

Retooling climate science for risk assessment

<p>Over recent years, climate change has become a global issue, leading political agendas and projecting onto almost every economic and development decision made today.  However, the way that we conduct climate science has remained broadly unchanged since the publication of the first IPCC report in 1990 - still relying on an ensemble of opportunity of climate models which doesn't allow for an estimation of high-impact tail risks and a highly idealized scenario framework which fails to test the fundamental technological assumptions which underpin our remaining pathways for achieving the Paris Agreement.  Here, we discuss how our strategy within the Make Our Planet Great Again "RISCCi" project is attempting to reframe the simulation of climate projections such as to provide better guidance for robust decision-making by categorizing the deep uncertainties of climate projections and mitigation pathways.  We present the initial results from an CNRM ensemble project which seeks to explore tail behaviour in climate feedbacks and impacts, and outline in a wider sense how future work and climate assessment needs to respond to the growing and evolving needs of a society as it works to minimise, and adapt to, climate change.</p>

Modelling the tail behaviour of precipitation aggregates using conditional spatial extremes.

<p>Fluvial flooding is not caused by high intensity rainfall at a single location, rather it is caused by the extremes of precipitation events aggregated over spatial catchment areas. Accurate modelling of the tail behaviour of such events can help to mitigate the financial aspects associated with floods, especially if river defences are built within specification to withstand an <em>n</em>-year event of this kind. Within an extreme value analysis framework, univariate methods for estimating the size of these <em>n</em>-year events are well studied and cemented in asymptotic theory.</p><p> To complement these techniques, we develop a high-resolution spatial model for extreme precipitation by providing a fully spatial extension of the conditional approach for modelling multivariate extremes. We simulate realistic precipitation fields from this model and use univariate techniques to make inference about the extremal behaviour of aggregates over specified spatial domains. The challenge of zero precipitation data is overcome and further applications of the model are discussed. The model is fit to data from a convection permitting forecast model within the 2018 UK Climate Projections (UKCP18).</p>

Tail asymptotics of an infinitely divisible space-time model with convolution equivalent Lévy measure

We consider a space-time random field on ${{\mathbb{R}^d} \times {\mathbb{R}}}$ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.

Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments

We study the tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.

Multivariate stochastic dominance applied to sector-based portfolio selection

In this study, we investigate whether sector-weighted portfolios based on alternative parametric assumptions are consistent with multivariate stochastic dominance (MSD) conditions for a class of non-satiable risk-averse investors. Focusing specifically on stable symmetric and Student’s t distributions, we propose and motivate an MSD rule to determine a partial order among sectors, based on a comparison between (i) location, (ii) dispersion parameters and (iii) either stability indices (for stable symmetric distributions) or degrees of freedom (for Student’s t distributions). The proposed MSD rule is applied to the US equity market to evaluate whether and how the derived stochastic dominance conditions are relevant to investors’ decisions. The empirical study confirms that the proposed MSD rule is effective and that the tail behaviour of returns is relevant to the optimization of portfolios for non-satiable investors.