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59
Evaluating the andersondarling distribution
 Proc
, 2004
"... Except for n=1, only the limit as n!1 for the distribution of the AndersonDarling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here ..."
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Except for n=1, only the limit as n!1 for the distribution of the AndersonDarling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracydirectly, via series with twoterm recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010. 1
Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
, 2013
"... manuscript (Please, provide the mansucript number!) Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. ..."
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Cited by 16 (8 self)
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manuscript (Please, provide the mansucript number!) Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.
Computing the TwoSided KolmogorovSmirnov Distribution
"... We propose an algorithm to compute the cumulative distribution function of the twosided KolmogorovSmirnov test statistic Dn and its complementary distribution in a fast and reliable way. Different approximations are used in different regions of (n, x). Java and C programs are available. Keywords: K ..."
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We propose an algorithm to compute the cumulative distribution function of the twosided KolmogorovSmirnov test statistic Dn and its complementary distribution in a fast and reliable way. Different approximations are used in different regions of (n, x). Java and C programs are available. Keywords: KS test, KolmogorovSmirnov distribution, goodnessoffit. 1.
The Modified Tempered Stable Distribution, GARCHModels and Option
 Business Engineering University of Karlsruhe
, 2006
"... and the Deutschen Forschungsgemeinschaft. †Michele Leonardo Bianchi’s research was supported by a Ph.D. scholarship of the University of Bergamo. 1 We introduce a new variant of the tempered stable distribution, named the modified tempered stable (MTS) distribution and we develop a GARCH option pri ..."
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and the Deutschen Forschungsgemeinschaft. †Michele Leonardo Bianchi’s research was supported by a Ph.D. scholarship of the University of Bergamo. 1 We introduce a new variant of the tempered stable distribution, named the modified tempered stable (MTS) distribution and we develop a GARCH option pricing model with MTS innovations. This model allows the description of some stylized empirical facts observed in financial markets, such as volatility clustering, skewness, and heavy tails of stock returns. To demonstrate the advantages of the MTSGARCH model, we present the results of the parameter estimation. Key words: option pricing, GARCH process, tempered stable distribution, volatility clustering 1
Chaffiol A: On goodness of fit tests for models of neuronal spike trains considered as counting processes
 Journal of Mathematical Neuroscience (2014) 4:3 Page 39 of 41
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Tempered stable and tempered infinitely divisible GARCH models
"... Abstract. In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as vola ..."
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Abstract. In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the nonzero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the riskneutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices.
A New Tempered Stable Distribution and Its Application to Finance. forthcoming
 in Georg Bol, Svetlozar T. Rachev, and Reinold Wuerth (Eds.), Risk Assessment: Decisions in Banking and Finance, Physika
, 2007
"... 1 In this paper, we will discuss a parametric approach to riskneutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the hi ..."
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1 In this paper, we will discuss a parametric approach to riskneutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the historical estimates. To this end, we introduce a new tempered stable distribution we refer to as the KR distribution. Some properties of this distribution will be discussed in this paper, along with the advantages in applying it to financial modeling. Since the KR distribution is infinitely divisible, a Lévy process can be induced from it. Furthermore, we can develop an exponential Lévy model, called the exponential KR model, and prove that it is an extension of the Carr, Geman, Madan, and Yor (CGMY) model. The riskneutral process is fitted by matching model prices to market
The signal within the noise: efficient inference of stochastic gene regulation models using fluorescence histograms and stochastic simulations
 Bioinformatics
, 2013
"... Motivation: In the noisy cellular environment, stochastic fluctuations at the molecular level manifest as cellcell variability at the population level that is quantifiable using high throughput singlecell measurements. Such variability is rich with information about the cell’s underlying gene regu ..."
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Motivation: In the noisy cellular environment, stochastic fluctuations at the molecular level manifest as cellcell variability at the population level that is quantifiable using high throughput singlecell measurements. Such variability is rich with information about the cell’s underlying gene regulatory networks, their architecture, and the parameters of the biochemical reactions at their core. Results: We report a novel method, called INSIGHT, for systematically combining highthroughput, timecourse flow cytometry measurements with computergenerated stochastic simulations of candidate gene network models to infer the network’s stochastic model and all its parameters. By exploiting the mathematical relationships between experimental and simulated population histograms, INSIGHT achieves scalability, efficiency, and accuracy while entirely avoiding approximate stochastic methods. We demonstrate our method on a synthetic gene network in bacteria and show that a detailed mechanistic model of this network can be estimated with high accuracy and high efficiency. Our method is completely general and can be used to infer models of signalactivated gene networks in any organism based solely on flow cytometry data and stochastic simulations. Availability: A free C source code implementing the INSIGHT algorithm, together with test data, is available from the authors. Contact:
Rational arithmetic Mathematica functions to evaluate the twosided one sample KS cumulative sample distribution
 Journal of Statistical Software
"... One of the most widely used goodnessoffit tests is the twosided one sample KolmogorovSmirnov (KS) test which has been implemented by many computer statistical software packages. To calculate a twosided p value (evaluate the cumulative sampling distribution), these packages use various methods ..."
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One of the most widely used goodnessoffit tests is the twosided one sample KolmogorovSmirnov (KS) test which has been implemented by many computer statistical software packages. To calculate a twosided p value (evaluate the cumulative sampling distribution), these packages use various methods including recursion formulae, limiting distributions, and approximations of unknown accuracy developed over thirty years ago. Based on an extensive literature search for the twosided one sample KS test, this paper identifies an exact formula for sample sizes up to 31, six recursion formulae, and one matrix formula that can be used to calculate a p value. To ensure accurate calculation by avoiding catastrophic cancelation and eliminating rounding error, each of these formulae is implemented in rational arithmetic. For the six recursion formulae and the matrix formula, computational experience for sample sizes up to 500 shows that computational times are increasing functions of both the sample size and the number of digits in the numerator and denominator integers of the rational number test statistic. The computational times of the seven formulae vary immensely but the Durbin recursion formula is almost always the fastest. Linear search is used to calculate the inverse of the cumulative sampling distribution (find the confidence interval halfwidth) and tables of calculated halfwidths are presented for sample sizes up to 500. Using calculated halfwidths as input, computational times for the fastest formula, the Durbin recursion formula, are given for sample sizes up to two thousand.
Robust EEG preprocessing for dependencebased condition discrimination
 Proceedings of the 33rd International Conference of the IEEE EMBS
, 2011
"... Abstract — This paper addresses the robustness of the filtering schemes in processing high resolution electroencephalogram (EEG) data in the context of discriminating two stimuli flickering at a given frequency. The raw data consists of recordings from a 128channel HydroCell GSN where the subject ..."
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Abstract — This paper addresses the robustness of the filtering schemes in processing high resolution electroencephalogram (EEG) data in the context of discriminating two stimuli flickering at a given frequency. The raw data consists of recordings from a 128channel HydroCell GSN where the subject was visually stimulated with two images flickering at 17.5 Hz, representing two distinct conditions, referred to as Face and Mock. These signals were then passed through a band pass filter to only capture the modulation at the flickering frequency, and a connectivity analysis was performed on the filtered signal using generalized measure of association, to observe if the network connectivity changes from one stimulus to the other. In this paper, we investigate the effect of the bandpass filter on the discriminability of the stimuli over different filter orders and quality factors. We observe that the network connectivity is stable over a significant range of parameter values of the filter, thus establishing the desired robustness. I.