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This paper studies the ruin probabilities in a homogeneous continuous compound Poisson risk model which is adapted for the perturbed insurance risk model with standard Brownian motion. In such a model, we construct a martingale in terms of a differentiable exponential function based on the discounted and perturbed surplus process. We obtain the exponential upper bounds for the ruin probabilities using Martingale approach and provide a sharper exponential upper bound for the infinite time ruin probability. Moreover, we derive two asymptotic approximation formulas for the finite time ruin probability when claim size distribution belongs to some heavy-tailed families. Finally, several numerical examples are presented to show the effect of constant force of interest on the ruin probabilities and that our results are excellent and reliable. [ABSTRACT FROM AUTHOR]

The discrete Pareto (DP) distribution studied in this paper is a probability model with a power-law tail, which provides a convenient alternative to the well-known Zipf distribution. While basic characteristics of the DP model are available explicitly, this is not an exponential family and parameter estimation connected with this model is a challenging task. With this in mind we develop a computational approach to this problem, based on the expectation-maximization (EM) algorithm. In the process, we discover an interesting new probability distribution, which is a certain tilted version of the standard gamma model, and we provide a short account of its basic properties. The latter play a crucial role in our EM algorithm. Our computational approach to DP parameter estimation is illustrated by simulations, while a real data example from finance illustrates potential applications of the DP stochastic model. [ABSTRACT FROM AUTHOR]

An α -slash distribution built upon a random variable X is a heavy tailed distribution corresponding to Y = X / U 1 / α , where U is standard uniform random variable, independent of X. We point out and explore a connection between α -slash distributions, which are gaining popularity in statistical practice, and generalized convolutions, which come up in the probability theory as generalizations of the standard concept of the convolution of probability measures and allow for the operation between the measures to be random itself. The stochastic interpretation of Kendall convolution discussed in this work brings this theoretical concept closer to statistical practice, and leads to new results for α -slash distributions connected with extremes. In particular, we show that the maximum of independent random variables with α -slash distributions is also a random variable with an α -slash distribution. Our theoretical results are illustrated by several examples involving standard and novel probability distributions and extremes. [ABSTRACT FROM AUTHOR]

In this follow up article of Arnold and Ghosh, we re-visit and study in details one of the two special cases of multivariate hidden truncation -(a) single variable truncation from above in a trivariate scenario where the component random variables follow an appropriate Pareto (type II) distribution. The case with single variable truncation was not discussed in details earlier in Arnold and Ghosh, in particular the estimation under both the classical and the Bayesian paradigm. It is well known that the Pareto distribution is a simple model for nonnegative data with a power law probability tail. Accumulating experience rapidly pointed out the fact that it is only in the upper tail of the income distributions that Pareto-like behavior can be expected. In practice, it has been observed that in income modeling and in other medical studies, quite often the observed data has been truncated with respect to several other unobserved co-variable(s) attaining certain critical levels. In this paper, we consider both the classical and the Bayesian inference (under the non-informative priors set up) of the resulting hidden truncated model. For illustrative purposes, a real data set on abalone is considered to show the flexibility of a single variable truncated Pareto (type II) distribution in a trivariate setting. Finally, the large sample behavior of the smallest order statistic in the case of a single co-variable truncation from above is provided in the appendix. [ABSTRACT FROM AUTHOR]

The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal probability metric of the second order is sharp. Some recent results concerning the convergence rates in Kolmogorov and Kantorovich metrics are extended as well. In contrast to many previous works, there are no assumptions that the summands of geometric sums are positive and have the same distribution. For the first time, an analogue of the Rényi theorem is established for the model of exchangeable random variables. Also within this model, a sharp estimate of convergence rate to a specified mixture of distributions is provided. The convergence rate of the appropriately normalized random sums of random summands to the generalized gamma distribution is estimated. Here, the number of summands follows the generalized negative binomial law. The sharp estimates of the proximity of random sums of random summands distributions to the limit law are established for independent summands and for the model of exchangeable ones. The inverse to the equilibrium transformation of the probability measures is introduced, and in this way a new approximation of the Pareto distributions by exponential laws is proposed. The integral probability metrics and the techniques of integration with respect to sign measures are essentially employed. [ABSTRACT FROM AUTHOR]

Asymptotic Ruin Probabilities in the Cramér-Lundberg model has been widely studied when the claims have light-tailed or heavy-tailed distributions. However, it has not been studied for extreme values over some threshold. In this paper, we investigate the use of the peaks over threshold method, to construct a new estimator of the ruin probability for a risk process with heavy tails claims amounts with infinite variance for the stationary arrival claims in an infinite time. Our approach is based on approximating the sample over some threshold by the generalized Pareto distribution. We prove that the proposed estimator is consistent and asymptotically normal. The performance of our new estimator is illustrated by some results of simulations for some loss models and provides an extensive example application to Danish data on large fire insurance. [ABSTRACT FROM AUTHOR]

The singular probability distributions that exist are insufficient to model naturally occurring events. Including the exponential distribution and the one-parameter Pareto distribution as a model for modelling real data. Therefore, there was a need to generalize and expand the probability distributions to develop the effectiveness of the distributions by adding one or more new parameters. Therefore, in this paper, we will introduce (Topp Leone G-Pareto distribution (TLG-P)) as a new model with two parameters (β,θ) based on the proposed family (Topp Leone G family). Therefore, the sum of the mathematical properties such as the central and eccentric moments and the moment-generating function. We will used maximum likelihood method. Moreover, the practical application of real data based on the proposed method. We can be employed for showing this distribution better compared to other distributions. [ABSTRACT FROM AUTHOR]

Several scientific fields including psychology are undergoing a replication crisis. There are many reasons for this problem, one of which is a misuse of p-values. There are several alternatives to p-values, and in this article we describe a complement that is geared toward replication. In particular, we focus on confidence intervals for the probability that a parameter estimate will exceed a specified value in an exact replication study. These intervals convey uncertainty in a way that p-values and standard confidence intervals do not, and can help researchers to draw sounder scientific conclusions. After briefly reviewing background on p-values and a few alternatives, we describe our approach and provide examples with simulated and real data. For linear models, we also describe how confidence intervals for the exceedance probability are related to p-values and confidence intervals for parameters. [ABSTRACT FROM AUTHOR]

Twelve commonly used probability distributions are evaluated to identify the most suitable model that could provide accurate extreme rainfall estimates in Egypt. Three popular parameter estimation methods are applied: the method of moments, L-moments and maximum likelihood. The performance of the models is evaluated based on several numerical and graphical goodness-of-fit criteria. The proposed procedure is applied to annual maximum daily rainfall data from a network of 31 stations located in Egypt. The results indicate that no single distribution performed the best at all stations. Log-Normal, Log-Pearson Type III and Exponential are the top three distributions for the frequency analysis of daily annual extreme rainfalls in Egypt, i.e. they are selected as the "optimum" models for 23%, 19% and 19% of the total stations, respectively. In contrast, the distributions: Normal, Gumbel, Logistic and Generalized Logistic are not suitable for describing the extreme rainfalls in the country. The performances of both L-moments and maximum likelihood methods are almost equal and much better than that of the method of moments. Additionally, Depth-Duration-Frequency curves were established for 18 stations by using the "optimum" model, which can support the design of hydraulic structures. The findings from this study would be helpful for rainfall frequency analysis in similar arid countries. [ABSTRACT FROM AUTHOR]

The probability characteristics of the heliostat support column base shear are discussed, and related methods are used to determine whether the base shear is conformed to the Gaussian distribution under all working conditions. Then, three kinds of peak estimating methods are selected to calculate the peak base shear, and results are compared. It is found that the Generalized Pareto Distribution (GPD) method is the most suitable for calculating the peak value of the heliostat support column base shear. Finally, the variation law of peak values of heliostat support column base shear is obtained and the variation law of peak and mean base shear are compared. The judgment criterion of whether the heliostat support column base shear is conformed to the Gaussian distribution is obtained, Gaussian and Non-Gaussian regions are divided. The peak value of the heliostat support column base shear which is calculated by the GPD method and met the specified guarantee rate has high accuracy. It can be met the needs of engineering application. The analysis of the variation law of peak values of heliostat support column base shear can be a reference for engineering design and scientific research. • Study of probability characteristics of heliostat base shear is provided. • The criterion of whether the base shear is conformed to the Gaussian distribution. • GPD method is the most suitable method for calculating peak base shear of heliostat. • Positive and negative maximum peak base shear should be studied in design. [ABSTRACT FROM AUTHOR]

Recent flooding related to extreme precipitation in the UK has highlighted the importance of better understanding these events. Many studies have quantified annual exceedance probabilities (or return periods) for UK extreme daily precipitation using fixed regions (e.g., HadUKP) and region of interest (ROI) (e.g., Flood Estimation Handbook) approaches, although fewer have evaluated short‐duration events, which are important for flash flooding. Existing UK extreme precipitation regions are based on daily datasets which have different characteristics compared to sub‐daily extremes, and their application to quantify short‐duration extremes may therefore be inappropriate. We use a recently available, quality‐controlled hourly precipitation dataset for the UK from 1992 to 2014 to derive various extreme precipitation indices (e.g., annual maxima, 0.99 quantile) which are combined with additional climatological variables (e.g., temperature), geographical characteristics (e.g., latitude), and weather patterns (WPs) to characterize the UK hourly extreme precipitation climatology and to define five new hourly extreme regions. These regions fulfil regional homogeneity and discordancy statistical measures, and reflect the dynamical processes associated with the weather pattern categorisation defined over the UK and surrounding European area. Thereafter, we use regional frequency analysis (RFA) to fit generalized extreme value (GEV) and generalized Pareto (GP) distributions to 1 hr annual maxima (AMAX) and 0.99 quantile (Q99) precipitation, respectively, to calculate regional annual probability estimates (AEP) for 20%, 10%, and 2% (i.e., 5‐, 10‐, and 50‐year return periods). The new regions capture the spatial variation of hourly precipitation across the UK. Furthermore, the AEP estimates using both distributions are similar for each region. Finally, the WPs associated with the frequency and intensity of the most extreme hourly precipitation accumulations are not identical to results reported by others for daily precipitation. [ABSTRACT FROM AUTHOR]

The development and application of the Envelope Peak-over-Threshold (EPOT) method is summarized for the roll motion of a ship in irregular waves. The method is based on the conventional Peak-over-Threshold (POT) method, but uses an envelope of the peaks for declustering the data. As suggested by a reduced-order model, a power-law tail should be applicable for the peaks of roll motions, which allows the introduction of physical considerations into the statistical model. A data-driven Generalized Pareto distribution (GPD) is applied to study the behavior of the shape parameter on large-volume samples in order to confirm the theoretical prediction of the tail structure. The physics-informed statistical model approximates data above a suitable threshold with a Pareto distribution, while the threshold is determined with a prediction error criterion. An example is included, where extrapolations with GPD are compared to the physics-informed model. • Application of Peak-over-Threshold method is considered where a time history envelope is used for declustering the data. • The study of behavior of distribution tails of roll motion peaks. • A physics-informed model with power-law, Pareto tail was formulated and applied to amplitudes of roll motions. [ABSTRACT FROM AUTHOR]

We propose an approach to solving the problem of optimizing the reliability of complex systems using Buffered Probability of Exceedance (bPOE). As a research subject, we consider the model of optimal control of oscillations of a hinged beam with random defects. This example shows that minimizing bPOE in reliability optimization problems is more preferable than minimizing the classical probability of exceedance. [ABSTRACT FROM AUTHOR]

The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains. [ABSTRACT FROM AUTHOR]

Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the parameters range, the two models can show up a recurrence/transience transition and, in the critical case, a positive/null recurrence transition. The collapse transition probabilities are chosen in such a way that the models are exactly solvable and, in case of positive recurrence, intimately related to the extended Sibuya and Pareto–Zipf distributions whose divisibility and self-decomposability properties are shown relevant. The study includes: existence and shape of the invariant measure, time-reversal, return time to the origin, contact probability at the origin, extinction probability, height and length of the excursions, a renewal approach to the fraction of time spent in the catastrophic state, scale function, first time to collapse and first-passage times, divisibility properties. [ABSTRACT FROM AUTHOR]

In sport, order-statistics-based models such as Henery's gamma model and the Thurstone–Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between two or more players. They can also be applied in many other areas, such as analysis of consumer preference data, which would be useful to marketing management. Two new families of such models derived from the exponentiated exponential, and Pareto distributions are introduced. Use of order-statistics-based models when there are more than two competitors has been hampered by lack of an efficient method of computation of outcome probabilities as a function of competitor strengths, and a fast method of computation of outcome probabilities is presented, which exploits the fact that the integral to be evaluated is an iterated integral. [ABSTRACT FROM AUTHOR]

Floods are the most destructive among all hazards across the globe. Research revealed that there is a marked increase in frequency and intensity of floods. Therefore, it is important to assess flood risk and reduce its probability and negative consequences. Assessment of flood probability helps to identify those areas which are very likely to be flooded in future. The current study attempts to assess the probability of floods by studying the causes, nature and intensifying factors in district Peshawar. In order to achieve the desired objectives, primary data regarding flood hazard were collected in a questionnaire survey, field observation and interviews of the relevant community and departments. Whereas secondary data were taken from Satellite images, irrigation department and Pakistan Meteorological Department. Flood hazard probability was determined for different return periods by developing flood scenarios. The Flood-2008 in the study area was considered as a landmark event for these scenarios. For visual interpretation, four different return periods of 5, 10, 50 and 100 years were mapped. Fast expansion in the built-up areas and other developmental works, violation of landuse planning and presence of bottlenecks (flood intensifying conditions) were found as main causative factors for the probability of flood hazard in the area under investigation. On the basis of findings from this study, it is recommended to build check dams or reservoirs in the upstream area, and a proper flood forecasting and warning system must be established. Furthermore, it is also recommended to implement the landuse planning regulations in the flood plain, in order to reduce the probability of flood. [ABSTRACT FROM AUTHOR]

Estimation of quantiles of Annual Maximum Wind Speed (AMWS) is needed in different environmental fields, engineering risk analysis, design of structures, renewable energy sources, agricultural operations, and climatology. Therefore, wind speed frequency analysis (WSFA) was carried out at nine stations from Pakistan. Multiparameter Probability Distributions (PDs), such as Generalized logistic (GLO), Generalized Extreme Value (GEV), Generalized Normal (GNO), Generalized Pareto (GPA), Weibull (WEI), Pearson type 3 (P3), Log Pearson type 3 (LP3); and two parameter PDs, such as Logistic (LOG), Normal (NOR), Gumbel (GUM), Exponential (EXP), and Uniform (UNI) were used to determine the most suitable distributions for the nine stations. The method of L-moments was used for estimating parameters of the distributions. The Kolmogorov-Smirnov (KS) test, Anderson-Darling (AD) test, Minimum L-Kurtosis (ML-K) Difference Criterion, and L-moment ratio diagram (L-ratio diagram) showed that four distributions, namely GEV, GNO, GPA, and GLO were the most suitable distributions for different stations and were superior to the two-parameter distributions. The quantile estimates (design estimates) from multiparameter PDs provide information on how fast the maximum wind will pass through a certain place and hence are important for policy makers and planners in the design and construction of different structures. The Multivariate Diebold–Mariano (DM) test was applied to check the accuracy of design estimates from the best fitted PDs and results indicated that they were significantly different. • Identification and evaluation of the best model among different Probability distributions for Annual Maximum Wind Speed. • Evaluation of the resulting quantiles through relative absolute error measurement. • Evaluation of relative absolute error from different Probability distributions through Multivariate Diebold–Mariano test. • Identification of the stations likely to face maximum or minimum wind speed in the future. [ABSTRACT FROM AUTHOR]

We propose an extension of the regular Cox's proportional hazards model which allows the estimation of the probabilities of rare events. It is known that when the data are heavily censored, the estimation of the tail of the survival distribution is not reliable. To improve the estimate of the baseline survival function in the range of the largest observed data and to extend it outside, we adjust the tail of the baseline distribution beyond some threshold by an extreme value model under appropriate assumptions. The survival distributions conditioned to the covariates are easily computed from the baseline. A procedure allowing an automatic choice of the threshold and an aggregated estimate of the survival probabilities are also proposed. The performance is studied by simulations and an application on two data sets is given. [ABSTRACT FROM AUTHOR]

In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. In this study, a new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria. [ABSTRACT FROM AUTHOR]

Abstract In this study, a robust semi-parametric approach which involves combining the empirical distribution and Pareto model is applied for measuring the income distribution in Malaysia based on the survey data of household incomes for the years of 2007, 2009, 2012 and 2014. From our analysis, it is found that the Pareto model is well fitted to the top household incomes for all years considered, suggesting that this model is a suitable parametric distribution to describe the top household incomes in Malaysia. Based on the semi-parametric Gini, generalized entropy and Atkinson indices, it is found that the income inequality shows a decreasing trend over the period, indicating an improvement of income distribution in Malaysia. Moreover, the fitted semi-parametric Lorenz curves show that the economic pie of the high income group reduced slightly after being taken up by the low income group while there is no clear change for the middle household income group. Highlights • A robust semi-parametric approach provides good results for measuring income inequality. • PITSE method provides good parameter estimation of Pareto model in the presence of outliers. • Various inequality indices based on semi-parametric model are provided. [ABSTRACT FROM AUTHOR]

Sequencing of the T cell receptor repertoire is a powerful tool for deeper study of immune response, but the unique structure of this type of data makes its meaningful quantification challenging. We introduce a new method, the Gamma-GPD spliced threshold model, to address this difficulty. This biologically interpretable model captures the distribution of the TCR repertoire, demonstrates stability across varying sequencing depths, and permits comparative analysis across any number of sampled individuals. We apply our method to several datasets and obtain insights regarding the differentiating features in the T cell receptor repertoire among sampled individuals across conditions. We have implemented our method in the open-source R package powerTCR. [ABSTRACT FROM AUTHOR]

Cost-sensitive feature selection learning is an important preprocessing step in machine learning and data mining. Recently, most existing cost-sensitive feature selection algorithms are heuristic algorithms, which evaluate the importance of each feature individually and select features one by one. Obviously, these algorithms do not consider the relationship among features. In this paper, we propose a new algorithm for minimal cost feature selection called the rough sets and Laplacian score based cost-sensitive feature selection. The importance of each feature is evaluated by both rough sets and Laplacian score. Compared with heuristic algorithms, the proposed algorithm takes into consideration the relationship among features with locality preservation of Laplacian score. We select a feature subset with maximal feature importance and minimal cost when cost is undertaken in parallel, where the cost is given by three different distributions to simulate different applications. Different from existing cost-sensitive feature selection algorithms, our algorithm simultaneously selects out a predetermined number of “good” features. Extensive experimental results show that the approach is efficient and able to effectively obtain the minimum cost subset. In addition, the results of our method are more promising than the results of other cost-sensitive feature selection algorithms. [ABSTRACT FROM AUTHOR]

In this paper we give an example of a distribution va, which does not belong to the domain of attraction of any stable distribution. However, if X has distribution va, then the distribution of |X| belongs to the domain of attraction of an a-stable distribution. The distribution has a simple structure, and may be useful for pedagogical purposes. [ABSTRACT FROM AUTHOR]

Wireless ad hoc networks can experience extreme fluctuations in transmission traffic in the Internet of Things, which is widely used today. Currently, the most crucial issues requiring attention for wireless ad hoc networks are making the best use of low traffic periods, reducing congestion during high traffic periods, and improving transmission performance. To solve these problems, the present paper proposes a novel cross-layer transmission model based on decentralized coded caching in the physical layer and a content division multiplexing scheme in the media access control layer. Simulation results demonstrate that the proposed model effectively addresses these issues by substantially increasing the throughput and successful transmission rate compared to existing protocols without a negative influence on delay, particularly for large scale networks under conditions of highly contrasting high and low traffic periods. [ABSTRACT FROM AUTHOR]

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered. [ABSTRACT FROM AUTHOR]

Multifractal analysis offers a number of advantages to measure spatial economic segregation and inequality, as it is free of categories and boundaries definition problems and is insensitive to some shape-preserving changes in the variable distribution. We use two datasets describing Kyoto land prices in 1912 and 2012 and derive city models from this data to show that multifractal analysis is suitable to describe the heterogeneity of land prices. We found in particular a sharp decrease in multifractality, characteristic of homogenisation, between older Kyoto and present Kyoto, and similarities both between present Kyoto and present London, and between Kyoto and Manhattan as they were a century ago. In addition, we enlighten the preponderance of spatial distribution over variable distribution in shaping the multifractal spectrum. The results were tested against the classical segregation and inequality indicators, and found to offer an improvement over those. [ABSTRACT FROM AUTHOR]

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given. [ABSTRACT FROM AUTHOR]

The generalized Pareto distribution (GPD) has been widely used to model exceedances over a threshold. This article generalizes the method of generalized probability weighted moments, and applies this method to estimate the parameters of GPD. The estimator is computationally easy. Some asymptotic results of this method are provided. Two simulations are carried out to investigate the behavior of this method and to compare them with other methods suggested in the literature. The simulation results show that the performance of the proposed method is better than some other methods. Finally, this method is applied to analyze a real-life data. [ABSTRACT FROM AUTHOR]

A model describing crack length distribution is proposed on the basis of experimental laws governing the formation and growth of fatigue cracks in a flat specimen with multiple stress raisers. The density of this distribution corresponds to that of Pareto and can be used to describe the accumulation of scattered defects in a wide range of cracking scale. The critical values of Pareto distribution exponent, which correspond to the limit states of the multiple fracture of solid bodies, have been substantiated. [ABSTRACT FROM AUTHOR]

In this article, we estimate the parameters of exponential Pareto II distribution by two new methods. The first one is based on the principle of maximum entropy (POME) and the second is by Kullback–Leibler divergence of survival function (KLS). Monte Carlo simulated data are used to evaluate these methods and compare them with the maximum likelihood method. Finally, we fit this distribution to a set of real data by estimation procedures. [ABSTRACT FROM AUTHOR]

Fire activity in North American forests is expected to increase substantially with climate change. This would represent a growing risk to human settlements and industrial infrastructure proximal to forests, and to the forest products industry. We modelled fire size distributions in southern Québec as functions of fire weather and land cover, thus explicitly integrating some of the biotic interactions and feedbacks in a forest-wildfire system. We found that, contrary to expectations, land-cover and not fire weather was the primary driver of fire size in our study region. Fires were highly selective on fuel-type under a wide range of fire weather conditions: specifically, deciduous forest, lakes and to a lesser extent recently burned areas decreased the expected fire size in their vicinity compared to conifer forest. This has large implications for fire risk management in that fuels management could reduce fire risk over the long term. Our results imply, for example, that if 30% of a conifer-dominated landscape were converted to hardwoods, the probability of a given fire, occurring in that landscape under mean fire weather conditions, exceeding 100,000 ha would be reduced by a factor of 21. A similarly marked but slightly smaller effect size would be expected under extreme fire weather conditions. We attribute the decrease in expected fire size that occurs in recently burned areas to fuel availability limitations on fires spread. Because regenerating burned conifer stands often pass through a deciduous stage, this would also act as a negative biotic feedback whereby the occurrence of fires limits the size of nearby future for some period of time. Our parameter estimates imply that changes in vegetation flammability or fuel availability after fires would tend to counteract shifts in the fire size distribution favoring larger fires that are expected under climate warming. Ecological forecasts from models neglecting these feedbacks may markedly overestimate the consequences of climate warming on fire activity, and could be misleading. Assessments of vulnerability to climate change, and subsequent adaptation strategies, are directly dependent on integrated ecological forecasts. Thus, we stress the need to explicitly incorporate land-cover’s direct effects and feedbacks in simulation models of coupled climate–fire–fuels systems. [ABSTRACT FROM AUTHOR]

The recent availability of digital traces generated by phone calls and online logins has significantly increased the scientific understanding of human mobility. Until now, however, limited data resolution and coverage have hindered a coherent description of human displacements across different spatial and temporal scales. Here, we characterise mobility behaviour across several orders of magnitude by analysing ∼850 individuals’ digital traces sampled every ∼16 seconds for 25 months with ∼10 meters spatial resolution. We show that the distributions of distances and waiting times between consecutive locations are best described by log-normal and gamma distributions, respectively, and that natural time-scales emerge from the regularity of human mobility. We point out that log-normal distributions also characterise the patterns of discovery of new places, implying that they are not a simple consequence of the routine of modern life. [ABSTRACT FROM AUTHOR]

Characterization results have great importance in statistics and probability applications. Some characterizations of Pareto of the first kind and Pareto of the second kind distributions are presented by using conditional expectation in terms of their failure (hazard) rate. We also provide two characterization theorems based on the th truncated moments. [ABSTRACT FROM AUTHOR]

The housing prices in many Asian cities have grown rapidly since mid-2000s, leading to many reports of bubbles. However, such reports remain controversial as there is no widely accepted definition for a housing bubble. Previous studies have focused on indices, or assumed that home prices are lognomally distributed. Recently, Ohnishi et al. showed that the tail-end of the distribution of (Japan/Tokyo) becomes fatter during years where bubbles are suspected, but stop short of using this feature as a rigorous definition of a housing bubble. In this study, we look at housing transactions for Singapore (1995 to 2014) and Taiwan (2012 to 2014), and found strong evidence that the equilibrium home price distribution is a decaying exponential crossing over to a power law, after accounting for different housing types. We found positive deviations from the equilibrium distributions in Singapore condominiums and Zhu Zhai Da Lou in the Greater Taipei Area. These positive deviations are dragon kings, which thus provide us with an unambiguous and quantitative definition of housing bubbles. Also, the spatial-temporal dynamics show that bubble in Singapore is driven by price pulses in two investment districts. This finding provides a valuable insight for policymakers on implementation and evaluation of cooling measures. [ABSTRACT FROM AUTHOR]

In order to assess their relative merits in the context of the determination of metocean extremes, the annual maxima (AM) and the peaks over threshold (POT) approaches are compared in terms of their accuracy in estimating exceedance probabilities on the basis of time series with various lengths and with characteristic that mimic those of real time series, such as nonstationarity and serial dependence. Based on the results of this study, the use of the POT approach is recommended. Furthermore, the method of probability weighted moments (PWMs) is recommended for the estimation of the parameters of the generalized Pareto distribution (GPD). [ABSTRACT FROM AUTHOR]

Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size. [ABSTRACT FROM AUTHOR]

Understanding the factors influencing the degree of spatial overlap among conspecifics is important for understanding multiple ecological processes. Compared to terrestrial carnivores, relatively little is known about the factors influencing conspecific spatial overlap in snakes, although across snake taxa there appears to be substantial variation in conspecific spatial overlap. In this study, we described conspecific spatial overlap of eastern indigo snakes (Drymarchon couperi) in peninsular Florida and examined how conspecific spatial overlap varied by sex and season (breeding season vs. non-breeding season). We calculated multiple indices of spatial overlap using 6- and 3-month utilization distributions (UD) of dyads of simultaneously adjacent telemetered snakes. We also measured conspecific UD density values at each telemetry fix and modeled the distribution of those values as a function of overlap type, sex, and season using generalized Pareto distributions. Home range overlap between males and females was significantly greater than overlap between individuals of the same sex and male home ranges often completely contained female home ranges. Male home ranges overlapped little during both seasons, whereas females had higher levels of overlap during the non-breeding season. The spatial patterns observed in our study are consistent with those seen in many mammalian carnivores, in which low male-male overlap and high inter-sexual overlap provides males with greater access to females. We encourage additional research on the influence of prey availability on conspecific spatial overlap in snakes as well as the behavioral mechanisms responsible for maintaining the low levels of overlap we observed. [ABSTRACT FROM AUTHOR]

The length biased beta-Pareto distribution is a flexible model for nonnegative data with a power law probability tail. The objective of this article is to derive a parameter estimation for the length biased beta-Pareto distribution by maximum likelihood estimation and method of moments which investigates its inverse transformation. The results of parameter estimation from a Monte Carlo simulation shows that the method of moments provide sample mean of estimated parameters that are close to the true parameter values more than the maximum likelihood estimation. These methods are illustrated with an application from the exceedances of flood peaks of the Wheaton River near Carcross in the Yukon Territory data set. [ABSTRACT FROM AUTHOR]

This article is concerned with the comparison of Bayesian and classical testing of a point null hypothesis for the Pareto distribution when there is a nuisance parameter. In the first stage, using a fixed prior distribution, the posterior probability is obtained and compared with the P-value. In the second case, lower bounds of the posterior probability ofH0, under a reasonable class of prior distributions, are compared with the P-value. It has been shown that even in the presence of nuisance parameters for the model, these two approaches can lead to different results in statistical inference. [ABSTRACT FROM PUBLISHER]

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments. [ABSTRACT FROM AUTHOR]

This article deals with the estimation of the lognormal-Pareto and the lognormal-generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-generalized Pareto case, we propose a mixed approach combining maximum likelihood and probability weighted moments. Extensive simulations analyze the relative efficiencies of the methods in various setups. Finally, the techniques are applied to two real datasets in the actuarial and operational risk management fields. [ABSTRACT FROM PUBLISHER]

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria. [ABSTRACT FROM PUBLISHER]

The Pareto distribution is a simple model for non negative data with a power law probability tail. Income and wealth data are typically modeled using some variant of the classical Pareto distribution. In practice, it is frequently likely that the observed data have been truncated with respect to some unobserved covariable. In this paper, a hidden truncation formulation of this scenario is proposed and analyzed. A bivariate Pareto (II) distribution is assumed for the variable of interest and the unobserved covariable. Distributional properties of the resulting model are investigated. A variety of parameter estimation strategies (under the classical set up) are investigated. [ABSTRACT FROM PUBLISHER]

In this paper, we estimate a tail of the mixture of log-normal and inverse Gaussian distribution in order to model extreme historical losses. Good estimate of the tail is essential in reinsurance for choosing or pricing high-excess layer. Method is supported by extreme value theory. We derive useful estimates of value-at-risk and expected shortfall. We apply this methodology to some fire insurance data. [ABSTRACT FROM PUBLISHER]