Tail Loss Research Articles

Central counterparty capital and nondefault losses

This paper analyses the components of central counterparty (CCP) capital requirements and makes several observations on the potential for loss absorption. Our first observation on default losses appears to be widely understood in the industry: as long as the CCP is not prevented from following the standard loss waterfall in its rule book, any losses that arise directly from member defaults can be absorbed by using existing CCP resources together with rule book powers to allocate any excess losses back to surviving members. Our second observation is a new frequency/severity result on nondefault losses. These are losses that are not directly due to a member default or are not covered by the rule book: the chance that such a loss exceeds the regulatory capital actually held is a very rare (at most, a two in a thousand) event. Moreover, the expected shortfall of such an event is an insurable quantum of less than one year’s profit to the healthy CCP. In the absence of an empirical database on CCP losses, these observations are ultimately inferred from comparable loss data from the 2008 Bank for International Settlements Loss Data Collection Exercise and from tail loss severity parameters implicit in existing CCP regulatory capital requirements.

Risk-Taking and Tail Events Across Trading Institutions

We study the reaction of investors to tail events across trading institutions. We conduct experiments in which investors bid on a financial asset that delivers a small positive reward in more than 99% of the cases and a large loss otherwise. The baseline treatment uses a repeated BDM mechanism whereas the market treatment replaces the uniform draw of the BDM mechanism by a uniform draw over the bids of the other participants. Our design is such that bids should not differ across treatments in normal times while allowing for potential differences to emerge after tail events have occurred. We find that markets tend to exacerbate the reaction of investors to tail losses and we attribute this effect to emotions.

Preference Robust Distortion Risk Measure and Its Application

Distortion risk measure (DRM) plays a crucial role in risk measuring and managing, especially in insurance pricing. Various DRMs have been introduced but little is discussed about which DRM at hand should be chosen to address a decision maker (DM)'s risk attitude. This paper aims to fill out the gap. Specifically we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk attitude is ambiguous. We introduce a preference robust distortion risk measure (PRDRM) which is based on the worst-case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well-known general principals such as concavity and inverse S-shapedness of distortion functions (over-weighting on events from impossible to possible or possible to certainty and under-weighting on those from possible to more possible) as well as new user-specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelop of a set of points to characterise the curvature of the distortion function and derive a tractable reformulation of the PRDRM when the underlying random loss is discretely distributed. Moreover, we show that the worst-case distortion function is a non-decreasing piece-wise linear function and can be determined by solving a linear programming problem. Finally, we apply the proposed PRDRM to a risk capital allocation problem and carry out some numerical tests to examine the efficiency of the PRDRM model.

Financial Risk Meter Based on Expectiles

The Financial Risk Meter (FRM) is an established quantitative tool that, based on conditional Value at Risk (VaR) ideas, yields insight into the dynamics of network risk. Originally, the FRM has been composed via Lasso based quantile regression, but we here extend it by incorporating the idea of expectiles, thus indicating not only the tail probability but rather the actual tail loss given a stress situation in the network. The expectile variant of the FRM enjoys several advantages: Firstly, the multivariate tail risk indicator conditional expectile-based VaR (CoEVaR) can be derived, which is sensitive to the magnitude of extreme losses. Next, FRM index is not restricted to an index compared to the quantile based FRM mechanisms, but can be expanded to a set of systemic tail risk indicators, which provide investors with numerous tools in terms of diverse risk preferences. The power of FRM also lies in displaying the FRM distribution across various entities every day. Two distinct patterns can be discovered under high stress and during stable periods from the empirical results in the United States stock market. Furthermore, the framework is able to identify individual risk characteristics and to capture spillover effects in a network.

Quantification of Cyber Risk – Risk Categories and Business Sectors

This white paper presents analysis of Advisen Cyber Loss dataset (www.advisenltd.com/data/cyber-loss-data/) containing a historical view of cyber events, collected from reliable and publicly verifiable sources. The dataset analyzed in this study comprehends 132,126 cyber events during 2008-2020, affecting 49,496 organizations, with more than 80% of the organizations represented in the dataset residing in the USA. A summary of the findings is provided as follows: - Currently, data collection and databases on losses from cyber events have an unbalanced recording of samples with the strongest emphasis on developing the US. centric data collection. However, cyber risk is international in nature affecting both commercial and private industry as well as government agencies across all sectors of the economy. Therefore, we advocate that a concerted effort be made to develop an adequate measurement and modelling process for cyber-related risks in the domestic landscape, there is a strong need and utility to be gained by collecting such data specifically for Australia. - There are many cyber risk classifications, each designed with specific intent, purpose, and which build on pre-existing laws and policies. Enterprises and market participants should adopt the cyber risk classification that best fits their needs; standardisation within sectors makes sense but standardisation across different sectors may be ineffective. - Over 60% of companies that recorded cyber-related losses have suffered from cyber-attacks more than once in the period 2008-2020. This suggests that governance processes relating to mitigation of such events can significantly be enhanced and that regulation and reporting around best practices as it emerges could help mitigate repeated events of the same nature from reoccurring. - Losses from cyber related events are heavy-tailed. This means that while the majority of losses is typically relatively small (85% of events cause losses $1 billion. - There is no distinct pattern or clear-cut relationship between the frequency of events, the loss severity, and the number of affected records. Contrary to assumptions often made in practice, the reported loss databases don’t demonstrate a direct proportional relationship between total loss incurred from a cyber event and attributes from the event such as the number of compromised records (data records breached or stolen), the number of employees in a corporation or the number of units of a company affected. This finding shows that all companies, no matter the volume or size of data record can be susceptible to significant incurred loss from cyber events. - The frequency and severity of the events depend on the business sector and type of cyber threat. - It is clear that even with the increased scrutiny and increased regulatory guidance the rate of cyber crime has not abated. In fact the frequency of reported cyber-related events has substantially increased between 2008 and 2016 (4,800 reported events in 2008, 16,800 reported events in 2016). Furthermore, the reporting of such events for modelling purposes could be enhanced as there appears to be a significant delay in the reporting of events that needs to be taken into account when drawing conclusions on the risks. - The most significant cyber loss event category, by number of events, continues to be Privacy - Unauthorized Contact or Disclosure and Data – Malicious Breach. Data related breaches have become increasingly more common since 2008, while Cyber Extorsion, Phishing, Spoofing and other Social Engineering practices also continue to increase, the pace at which malicious breach related events has occurred has now surpassed these other prominent categories of loss event risk type in recent years. - The heavy tailed nature of cyber loss continues to be present. This is directly observed by the fact that cyber loss are well represented by the expression “one loss causes ruin” adage attributed to heavy tailed loss processes that demonstrate regular variation or power lower severity tail behaviour. As such, in all categories of cyber loss type and in all sectors of the economy it was found that loss severity is often dominated by large individual events. Overall, data breaches have caused the most serious financial consequences in the last four years, while the Information sector, Professional Scientific & Technical Services, and Finance & Insurance have suffered most of the financial damage during the sample period 2008-2020.

Correction to 'Substrate use drives the macroevolution of mammalian tail length diversity'.

You have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Mincer S. T. and Russo G. A. 2020Correction to ‘Substrate use drives the macroevolution of mammalian tail length diversity’Proc. R. Soc. B.2872020247720202477http://doi.org/10.1098/rspb.2020.2477SectionYou have accessCorrectionsCorrection to ‘Substrate use drives the macroevolution of mammalian tail length diversity’ S. T. Mincer S. T. Mincer http://orcid.org/0000-0003-2275-7971 Google Scholar Find this author on PubMed Search for more papers by this author and G. A. Russo G. A. Russo Google Scholar Find this author on PubMed Search for more papers by this author S. T. Mincer S. T. Mincer http://orcid.org/0000-0003-2275-7971 Google Scholar Find this author on PubMed Search for more papers by this author and G. A. Russo G. A. Russo Google Scholar Find this author on PubMed Search for more papers by this author Published:28 October 2020https://doi.org/10.1098/rspb.2020.2477See original article.Substrate use drives the macroevolution of mammalian tail length diversityProc. R. Soc. B287, 20192885. (Published 5 February 2020). (doi:10.1098/rspb.2019.2885)There are two minor errors in figure 2 of the originally published manuscript. The scale colour bar accompanying the summary tree to signify slope value was flipped so that it was incorrectly labelled. In the corrected figure red represents slope of −4.4, and blue represents slope of 3.3. The labels for two branches in the summary tree representing significant shifts in slope and intercept for Caprinae and Bovinae were also switched. Correct slope and intercept values for all branches are included in the electronic supplementary material, and the errors described here have now been fixed in the figure submitted in this correction. These errors do not change the interpretation or accuracy of results. Figure 2. Summary tree of the evolutionary best-fit model for tail length ∼ body length. Black represents the ancestral condition and each colour represents a statistically significant evolutionary shift (regime) in slope and intercept (available in electronic supplementary material), coloured by the slope for each group. Tailless species (dashed lines) were not included in the evolutionary best-fit model but have been subsequently added back onto the tree to show where tail loss has occurred in phylogeny.Download figureOpen in new tabDownload PowerPoint Previous Article FiguresRelatedReferencesDetailsRelated articlesSubstrate use drives the macroevolution of mammalian tail length diversityFeb 5, 2020, 12:00:00 AMProceedings of the Royal Society B: Biological Sciences This Issue28 October 2020Volume 287Issue 1937 Article InformationDOI:https://doi.org/10.1098/rspb.2020.2477PubMed:33109016Published by:Royal SocietyPrint ISSN:0962-8452Online ISSN:1471-2954History: Published online28/10/2020Published in print28/10/2020 License:© 2020 The Author(s)Published by the Royal Society. All rights reserved. Citations and impact Subjectsevolution Large datasets are available through Proceedings B's partnership with Dryad

‘Tail’ autotomy and consequent stinger loss decrease predation success in scorpions

Predation success depends on factors such as hunger, prey size, prey availability and intensity of competition. A neglected factor that may also influence predation success is the proper function of morphological traits related to prey search, capture and manipulation. Injuries that compromise the functionality of these morphological traits may reduce predation success. In many invertebrates, autotomy can compromise predation success because the detached body part may be crucial for hunting. However, empirical evidence linking autotomy and predation success is relatively scarce. We filled this gap using the scorpion Ananteris balzani, which autotomizes the last abdominal segments, known as the ‘tail’. This is a unique form of autotomy as ‘tail’ autotomy implies the loss of the stinger, an organ used for venom inoculation, which is the main form of large prey subjugation. Using a paired experimental design, we found that for both small and large prey, subduing success was higher when individuals were intact than when they were autotomized. After autotomy, subduing success of male scorpions decreased from 90% to 17% for small prey and from 47% to 1% for large prey. Subduing success of female scorpions after autotomy decreased from 98% to 93% for small prey and from 97% to 70% for large prey. Autotomized individuals took longer than intact individuals to subdue both small and large prey, but the effect size was higher for large prey. Considering that the tail does not regenerate, autotomized individuals (especially males) will experience a lifelong reduction in trophic niche breadth because their diet will be mostly composed of small prey. Moreover, autotomized individuals probably move more to enhance the likelihood of finding small prey, which may increase their exposure to predators and consequently the costs related to tail loss.

Expression of acid-labile subunit (ALS) in developing and adult zebrafish and its role in dorso-ventral patterning during development

Mammalian acid-labile subunit (ALS) is a serum protein that binds binary complexes between Insulin-like growth factors (IGFs) and Insulin-like growth factor-binding proteins (IGFBPs) extending their half-life and keeping them in the vasculature. Human ALS deficiency (ACLSD), due to homozygous or compound heterozygous mutations in IGFALS, leads to moderate short stature with reduced levels of IGF-I and IGFBP-3. There is only one corresponding zebrafish ortholog gene and it has not yet been studied. In this study we elucidate the role of igfals during zebrafish development. In zebrafish embryos igfals mRNA is expressed throughout development, mainly in the brain and subsequently also in the gut and swimbladder. To determine its role during development, we knocked down igfals gene product using morpholinos (MOs). Igfals morphant embryos displayed dorsalization in different degrees of severity, including a shortened trunk and loss of tail. Furthermore, co-injection of human IGFALS (hIGFALS) mRNA was able to rescue the MO-induced phenotype. Finally, overexpression of either hIGFALS or zebrafish igfals (zigfals) mRNA leads to ventralization of embryos including a reduced head and enlarged tail. These findings suggest that als plays an important role in dorso-ventral patterning during zebrafish development.

PINK1 p.Leu347Pro mutations in Malays: Prevalence and illustrative cases

BackgroundAn improved understanding of the genetic determinants of Parkinson's disease (PD) in underrepresented populations, and better characterization of genotype-phenotype correlations in monogenic PD, are needed. Scarce literature exists regarding the genetic aetiology of PD in Malays, who comprise 200 million individuals in South-East Asia. Phenotypic data regarding PARK-PINK1 are also limited. MethodsA multi-ethnic cohort of PD patients from Malaysia (n = 499, including 185 Malays) were tested using a next-generation sequencing-based PD gene panel. The prevalence and clinico-radiological features of patients with the PINK1 p. Leu347Pro mutation are described. This mutation has previously only been reported in people of Filipino or Chamorro (native Guamanian) ancestry. ResultsHomozygous p. Leu347Pro mutations were found in five unrelated Malay patients, yielding a prevalence of 6.9% among Malays with PD onset ≤50 years (2.7% of the Malay group overall). This variant was not detected in the homozygous state in 300 Malay controls, but two were heterozygous carriers (0.67%) indicating a relatively high population frequency in keeping with the high frequency of PARK-PINK1 among Malay patients. Interesting clinical features were observed, e.g., differences in the age at PD onset and clinical progression, despite having the same point mutations. Previously unreported brain MRI abnormalities involving the corticospinal tract and hypothalamus, and “loss of the swallow tail” sign, were documented. ConclusionsThis report contributes to the very limited literature on PD genetics in the Malay population, and more broadly to the epidemiological, phenotypic and neuroimaging characterization of PARK-PINK1. It also further supports the pathogenicity of the p. Leu347Pro variant.

Dependence and risk spillovers between green bonds and clean energy markets

In this study, we first examine the dynamic dependence structure between green bonds (GBs) and several global and sectoral clean energy (CE) markets by using several time-invariant and time-varying copula approaches over the period from 5 July 2011 to 24 February 2020. We then apply conditional value-at-risk (CoVaR) and delta CoVaR to capture downside and upside risk spillovers from CE to GB, and vice versa. Our empirical analysis shows that there is positive time-varying average and tail dependence between GBs and CE stock markets. Moreover, extreme downward or upward movements in the CE stock market have a spillover effect on the GB market, and vice versa. Furthermore, the risk spillover between these markets is asymmetric. These results make an important contribution to policymakers and environmentally friendly investors with GB positions by adding unexpected tail losses. It is critical for the GB investors to invest their capital effectively in economic activities that are consistent with a low-carbon economy.

Sand lizards Lacerta agilis with higher digit ratios are more likely to autotomy.

Digit ratio is a morphological feature regarded as a biomarker of the balance of sex hormones during early development. The exposure of embryos to a set of sex hormones and the mutual relations between those hormones cause the emergence of individual morphological and/or behavioural characteristics as well as differences between sexes. We have thus hypothesised that differences in one of these morphological traits-digit ratio-may be a proxy representing a tendency towards tail autotomy. The aim of this study is to investigate the digit ratio (2D:3D, 2D:4D, 3D:4D) of the sand lizard, Lacerta agilis, Lacertidae, a species characterised by well-developed sexual dimorphism, whereby females are larger than males. We also tested associations between patterns in digit ratio and caudal autotomy, a common defensive mechanism among lizards. To our knowledge, the relationship between a tendency towards autotomy and digit ratio pattern has never been researched. To date, studies on autotomy have mainly focused on the consequences, costs or evolutionary background of tail loss. Hence, researchers examined mostly the frequency of autotomy in the context of predatory pressure or habitat conditions, omitting an individual's behavioural tendency to shed its tail. However, behavioural traits can affect an individual's exposure to predator attack and consequently the need to use an anti-predator strategy. Thus, following this logic, dropping the tail may be the result of the lizard's intraspecific personality characteristics, resulting from the effect of hormones on behaviour or innate traits. Therefore, we suggest that the inclusion of autotomy as a factor explaining observed digit ratio patterns and their variability between taxa has great potential. We used computerised measurements of photographed limbs to determine the length of digits. We found that the digit ratios for all four limbs were significantly lower in females than in males, excluding the 3D:4D ratio for the right hindlimbs. Therefore, the results confirmed the pattern already observed for most lizards. The novel element in our study is the detection of the relationship between a tendency towards caudal autotomy and digit ratio. Individuals with a tendency towards autotomy have a higher 2D:4D ratio in the right forelimbs and a lower 2D:3D ratio in the right hindlimbs. Obtained results suggest that these morphological characteristics are most likely related to intraspecific differences (between bold and shy individuals) which consequently may determine an individual's reaction or susceptibility to be a prey and escape behaviour. Thus, our results are probably the first attempt to link digit ratio to the susceptibility of lizards to tail autotomy.

The movement dynamics of autotomized lizards and their tails reveal functional costs of caudal autotomy.

Autotomy has evolved independently several times in different animal lineages. It frequently involves immediate functional costs, so regeneration evolved in many instances to restore the functionality of that body part. Caudal autotomy is a widespread antipredator strategy in lizards, although it may affect energy storage, locomotion dynamics, or survival in future encounters with predators. Here, we assessed the effect of tail loss on the locomotor performance of wall lizards (Podarcis muralis), as well as the recovery of locomotor functionality of lizards with regenerated tails, and the movement dynamics of shed tails that were either intact or having regenerated portions. Tail loss had no effect on locomotion over unhindered spaces, possibly due to compensation between a negative effect on the stride of front limbs, and a positive effect of losing mass and friction force. We found a clear negative impact of tail loss on locomotion in spaces with interspersed obstacles, in which tailed lizards jumped larger distances when leaving the obstacles. Besides, lizards that used the tail to push off the ground were able to approach the obstacles from further, so that the tail seemed to be useful when used during jumping. Regeneration fully restores lizard's locomotor capacities, but tail antipredator value, as indicated by the intensity of post-autotomic movements, is only partially retrieved. From these results, we propose that, together with the recovery of post-autotomy antipredator capacities, the restoration of the organismal locomotor performance may have been an important, yet frequently neglected factor in the evolution of lizard's regeneration ability.

Tail Events, Emotions and Risk Taking

Recent works have shown how tail events could account for financial anomalies such as the equity premiumpuzzle. These models do not explore, however, why investors would discount tail risk so heavily. We take on this challenge by designing a novel tail-event experiment to assess both investors' behavioral and physiological reactions. We show that investors who observe the tail event without suffering losses tend to decrease their pricing of the asset subsequently. By contrast, loss-averse investors who suffer tail losses tend to increase their bids. This response is especially pronounced for those who exhibit a strong emotional response to tail losses. This demonstrates the key role played by emotions in influencing investors' response to tail events. Finally, investors who exhibit high anticipatory arousal, as measured with electrodermal activity, posted lower bids and were less likely to suffer tail losses and go bankrupt. They also achieved higher earnings when tail events occurred frequently. This finding contrasts with the common view that investors should silence their emotions.

Importance sampling with splitting for portfolio credit risk

We consider a credit portfolio with highly skewed exposures. In the portfolio, small number of obligors have very high exposures compared to the others. For the Bernoulli mixture model with highly skewed exposures, we propose a new importance sampling scheme to estimate the tail loss probability over a threshold and the corresponding expected shortfall. We stratify the sample space of the default events into two subsets. One consists of the events that the obligors with heavy exposures default simultaneously. We expect that typical tail loss events belong to the set. In our proposed scheme, the tail loss probability and the expected shortfall corresponding to this type of events are estimated by a conditional Monte Carlo, which results in variance reduction. We analyze the properties of the proposed scheme mathematically. In numerical study, the performance of the proposed scheme is compared with an existing importance sampling method.

Range Limits and Demography of a Mountaintop Endemic Salamander and Its Widespread Competitor

Range limits can be caused by a multitude of abiotic or biotic factors, but all of these must act through the demography of range-edge populations. Woodland salamanders of the genus Plethodon often exhibit distinct range boundaries where the distributions of competing species meet. Because of their high densities and low mobility, Plethodon are well suited for studies of how fitness-related traits change as species approach their range limits. Across contact zones between the mountaintop endemic Peaks of Otter Salamander (Plethodon hubrichti) and the widespread Eastern Redback Salamander (Plethodon cinereus), we measured changes in three salamander traits: 1) body condition, 2) frequency of tail loss, and 3) proportion of hatchlings. We then used hierarchical Bayesian models to compare these traits among five site types: allopatric sites for both species, sites where one of the species was dominant and the other was rare, and mixed sites containing high densities of both species. For P. hubrichti, we found no consistent changes in body condition across contact zones. However, frequency of tail loss increased continuously from allopatric sites (21%) to rare sites (54%). We also found evidence of reduced hatchling proportions at sites outside of allopatric areas (15–16% versus 30% at allopatric sites). For P. cinereus, body condition was higher at allopatric sites compared to sites within the contact zone. Similar to P. hubrichti, frequency of tail loss in P. cinereus increased continuously from allopatric sites (27%) to sites where P. cinereus were rare (50%). However, for P. cinereus, we did not find evidence of reduced hatchling numbers towards the edge of their range margin. Overall, our results suggest that both species likely have reduced fitness as they approach their range margin. Tail loss, which may reflect interference competition, effects of predation, or interactions between these, could potentially act as a density-dependent factor that stabilizes the range boundary between these species, at least over shorter time scales.

Multigenerational Exposures of Daphnia Magna to Pristine and Aged Silver Nanoparticles: Epigenetic Changes and Phenotypical Ageing Related Effects.

Engineered nanoparticles (NPs) undergo physical, chemical, and biological transformation after environmental release, resulting in different properties of the "aged" versus "pristine" forms. While many studies have investigated the ecotoxicological effects of silver (Ag) NPs, the majority focus on "pristine" Ag NPs in simple exposure media, rather than investigating realistic environmental exposure scenarios with transformed NPs. Here, the effects of "pristine" and "aged" Ag NPs are systematically evaluated with different surface coatings on Daphnia magna over four generations, comparing continuous exposure versus parental only exposure to assess recovery potential for three generations. Biological endpoints including survival, growth and reproduction and genetic effects associated with Ag NP exposure are investigated. Parental exposure to "pristine" Ag NPs has an inhibitory effect on reproduction, inducing expression of antioxidant stress related genes and reducing survival. Pristine Ag NPs also induce morphological changes including tail losses and lipid accumulation associated with aging phenotypes in the heart, abdomen, and abdominal claw. These effects are epigenetic remaining two generations post-maternal exposure (F2 and F3). Exposure to identical Ag NPs (same concentrations) aged for 6 months in environmentally realistic water containing natural organic matter shows considerably reduced toxicological effects in continuously exposed generations and to the recovery generations.

Tail Lesions and Losses of Docked and Undocked Pigs in Different Farrowing and Rearing Systems

This study aimed to investigate the effects of farrowing and rearing systems on tail lesions and losses of docked and undocked pigs. Pigs from three farrowing systems: Conventional farrowing crate (FC), free farrowing (FF) and group housing of lactating sows (GH) were randomly allocated to different rearing systems: A conventional system (CONV), where the pigs were regrouped and transferred to conventional finishing pens at ten weeks of age or a wean-to-finish (W-F) system, where the pigs remained in their pens until slaughter with higher space allowance during rearing. Weekly, tail lesions and losses were assessed individually. The incidence of tail lesions was higher in undocked CONV pigs compared to undocked W-F pigs (maximum: CONV 58.01%, W-F 41.16%). The rearing system had a significant effect on tail losses at the end of finishing (CONV 67.63%, W-F 38.2%). The significant effect of the rearing system might be explained by higher space allowance during rearing and reduced regrouping stress for W-F pigs. In conclusion, farrowing systems showed no effects, but the W-F rearing system reduces the frequency of tail lesions and losses; the curves of tail lesions increased slower and stayed on a lower level, which resulted in lower losses as well.

A new family of heavy tailed distributions with an application to the heavy tailed insurance loss data

Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuaries often search for new and appropriate statistical models to address data related to financial risk problems. In this work, we propose a new family of heavy tailed distributions. Some basic properties of this new family of heavy tailed distributions are obtained. A special sub-model of the proposed family, called a new heavy tailed Weibull model is considered in detail. The maximum likelihood estimators of the model parameters are obtained. A Monte Carlo simulation study is carried out to evaluate the performance of these estimators. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is done. Finally, an application of the proposed model to a heavy tailed insurance loss data set is presented.

Impacts of caudal autotomy on personality

Caudal autotomy, the voluntary shedding of a tail, is a last-ditch strategy used by many lizard species to escape from predators. There are several costs associated with caudal autotomy that may cause lizards to change their behaviour during tail regeneration. These behavioural changes may be dependent upon individual differences in response to autotomy (e.g. trait or state-dependent differences) and/or the degree of tail loss, as many lizards have the capacity to only partially shed their tail which probably entails fewer costs relative to complete autotomy. However, no study, to our knowledge, has considered how caudal autotomy, or the extent of autotomy, affects individual behavioural variation. Accordingly, we investigated the effects of both partial and complete tail loss on individual behavioural variation in delicate skinks, Lampropholis delicata. We found that lizards that experienced complete tail loss, on average, became less active and explorative and had much slower sprint speeds following autotomy. These lizards also became more predictable and consistent in their behaviour, exhibiting a notable decrease in their within-individual behavioural variance. In contrast, we did not see any significant behavioural effects in lizards that experienced partial tail loss. We also found a positive among-individual correlation between activity/exploration and neophilia, but tail loss had no effect on the structure of this syndrome. Our results suggest that complete tail loss may impose effects on traits more closely associated with locomotion and predator escape ability, while also constraining an individual's capacity for differential behavioural expression.

Substrate use drives the macroevolution of mammalian tail length diversity.

External length is one of the most conspicuous aspects of mammalian tail morphological diversity. Factors that influence the evolution of tail length diversity have been proposed for particular taxa, including habitat, diet, locomotion and climate. However, no study to date has investigated such factors at a large phylogenetic scale to elucidate what drives tail length evolution in and across mammalian lineages. We use phylogenetic comparative methods to test a priori hypotheses regarding proposed factors influencing tail length, explore possible interactions between factors using evolutionary best-fit models, and map evolutionary patterns of tail length for specific mammalian lineages. Across mammals, substrate use is a significant factor influencing tail length, with arboreal species maintaining selection for longer tails. Non-arboreal species instead exhibit a wider range of tail lengths, secondarily influenced by differences in locomotion, diet and climate. Tail loss events are revealed to occur in the context of both long and short tails and influential factors are clade dependent. Some mammalian groups (e.g. Macaca; primates) exhibit elevated rates of tail length evolution, indicating that morphological evolution may be accelerated in groups characterized by diverse substrate use, locomotor modes and climate.