A common approach to simulating a Lévy process is truncate its shot-noise representation. We focus on subordinators and introduce the remainder process, which represents jumps that are removed by truncation. characterize when these processes self-similar show that, in case, they can be indexed parameter α∈(−∞,1). When α∈(0,1), correspond α-stable distributions, α=0, certain generalizations of Dickman distribution. Thus, distribution plays role 0-stable this context.

One of the major points contention in studying and modelling financial returns is whether or not variance finite infinite (sometimes referred to as Bachelier–Samuelson Gaussian world versus Mandelbrot stable world). A different formulation question asks how heavy tails are. The available empirical evidence can be, has been, interpreted more than one way. apparent paradox, which puzzled many a researcher, that appear become less for frequent (e.g. monthly) daily) returns, phenomenon easily...

Modern measures of diversity satisfy reasonable axioms, are parameterized to produce profiles, can be expressed as an effective number species simplify their interpretation, and come with estimators that allow one apply them real-world data. We introduce the generalized Simpson's entropy a measure investigate its properties. show it has many useful features used biodiversity. Moreover, unlike most commonly indices, unbiased estimators, which for sound estimation poorly sampled, rich communities.

We extend the class of tempered stable distributions, which were first introduced in Rosiński (2007). Our new allows for more structure and variety tail behaviors. discuss various subclasses relations between them. To characterize possible tails, we give detailed results about finiteness moments. also necessary sufficient conditions tails to be regularly varying. This last part us domain attraction a particular distribution belongs.

In this letter, we introduce an estimator of Küllback-Leibler divergence based on two independent samples. We show that any finite alphabet, has exponentially decaying bias and it is consistent asymptotically normal. To explain the importance estimator, provide a thorough analysis more standard plug-in estimator. normal, but with infinite bias. Moreover, if modify to remove rare events cause become infinite, still decays at rate no faster than O(1/n). Further, extend our results estimating...

Abstract We propose a new methodology for testing the authorship of relatively small work compared with large body an author's cannon. Our approach is based on comparing entropy two samples. The difficulty lies in fact that known estimators tend to have bias even when sample size fairly large. To deal this, we suggest splitting larger into several parts length equal smaller work. then using these sub-samples simple non-parametric test. apply our test whether poem "Shall I Die?" which...

This paper serves a twofold purpose. First, unified perspective on diversity indices is introduced based an entropic basis. It shown that the class of all linear combinations basis, referred to as indices, covers wide range used in literature. Second, estimators for proposed and it these have rapidly decaying biases asymptotic normality.

Zhang in 2012 introduced a nonparametric estimator of Shannon’s entropy, whose bias decays exponentially fast when the alphabet is finite. We propose methodology to estimate this estimator. then use it construct new entropy. Simulation results suggest that adjusted has significantly lower than many other commonly used estimators. consider both case finite and countably infinite.

We give an explicit representation for the transition law of a tempered stable Ornstein–Uhlenbeck process and use it to develop rejection sampling algorithm exact simulation increments from this process. Our results apply general classes both univariate multivariate distributions contain number previously studied as special cases.

Mobility models are crucial for the simulation and evaluation of protocols multihop wireless networks. However, most commonly used mobility do not reflect way humans actually move. This significantly affects reliability results. In this paper we introduce a new model called Smoothly Truncated Levy Walk (STLW), which is more realistic than standard that appear in literature. Its main innovations as follows. First, to take into account dependencies direction motion, it changes instead...

We introduce a methodology for the simulation and parameter estimation of multivariate tempered stable distributions with an emphasis on bivariate case. Our approach is based approximation due to discretization spectral measure. It then applied two financial datasets related exchange rates. The first comprised rates between standard currencies, while second cryptocurrencies. results hold wide class infinitely divisible distributions.

For a probability distribution $P$ on an at most countable alphabet $\mathcal{A}$, this article gives finite sample bounds for the expected occupancy counts $\mathbb{E}K_{n,r}$ and probabilities $\mathbb{E}M_{n,r}$. Both upper lower are given in terms of counting function $\nu$ $P$. Special attention is to case where bounded by regularly varying function. In case, it shown that our general results lead optimal-rate control with explicit constants. Our also put perspective Turing's formula...

Stochastic knapsack problems deal with selecting items potentially random sizes and rewards so as to maximize the total reward while satisfying certain capacity constraints. A novel variant of this problem, where are worthless unless collected in bundles, is introduced here. This setup similar Groupon model, a off minimum number users sign up for it. Since optimal algorithm solve problem not practical, several adaptive greedy approaches reasonable time memory requirements studied detail -...

We consider two models of summation independent identically distributed random variables with a parameter. The first is motivated by financial applications and the second contact for species migration. characterize limiting distributions their bifurcations under different relationships between parameter number summands. find that in phase transition we may get are quite from those come up standard limit theorems. Our results suggest these provide better models, at least certain aggregation...

The flipped classroom pedagogy is a popular framework for teaching computing courses. This hinges on students completing the preparatory (prep) work before class. usually requires watching videos or reading several sections from textbook. To encourage to do prep work, short multiple-choice online quiz often given. However, despite this incentive, many not spend enough time work. deal with challenge, we introduce new approach that designed be more engaging. replaces regular textbook an...

Value-at-Risk (VaR) is one of the best known and most heavily used measures financial risk. In this paper, we introduce a non-iterative semiparametric model for VaR estimation called single index quantile regression time series (SIQRTS) model. To test its performance, give an application to four major US market indices: S&P 500 Index, Russell 2000 Dow Jones Industrial Average, NASDAQ Composite Index. Our results suggest that method has good finite sample performance often outperforms number...