12,231 research outputs found
Efficient and accurate algorithms for the computation and inversion of the incomplete gamma function ratios
Algorithms for the numerical evaluation of the incomplete gamma function ratios and are described for positive values of and . Also, inversion methods are given for solving the equations , , with . Both the direct computation and the inversion of the incomplete gamma function ratios are used in many problems in statistics and applied probability. The analytical approach from earlier literature is summarized, and new initial estimates are derived for starting the inversion algorithms. The performance of the associated software to our algorithms (the Fortran 90 module IncgamFI) is analyzed and compared with earlier published algorithms
Hedging error in Lévy models with a Fast Fourier Transform approach
We measure, in terms of expectation and variance, the cost of hedging a contingent claim when the hedging portfolio is re-balanced at a discrete set of dates. The basic point of the methodology is to have an integral representation of the payoff of the claim, in other words to be able to write the payoff as an inverse Laplace transform. The models under consideration belong to the class of Lévy models, like NIG, VG and Merton models. The methodology is implemented through the popular FFT algorithm, used by many financial institutions for pricing and calibration purposes. As applications, we analyze the effect of increasing the number of tradings and we make some robustness tests.Hedging, Lévy models, Fast Fourier Transform
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
We consider the asymptotic behavior of the incomplete gamma functions
gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are
needed to describe the transition area z~a in which case error functions are
used as main approximants. We use integral representations of the incomplete
gamma functions and derive a uniform equation by applying techniques used for
the existing uniform expansions for gamma(a,z) and Gamma(a,z). The result is
compared with Olver's uniform expansion for the generalized exponential
integral. A numerical verification of the expansion is given in a final
section
Hyper-g Priors for Generalized Linear Models
We develop an extension of the classical Zellner's g-prior to generalized
linear models. The prior on the hyperparameter g is handled in a flexible way,
so that any continuous proper hyperprior f(g) can be used, giving rise to a
large class of hyper-g priors. Connections with the literature are described in
detail. A fast and accurate integrated Laplace approximation of the marginal
likelihood makes inference in large model spaces feasible. For posterior
parameter estimation we propose an efficient and tuning-free
Metropolis-Hastings sampler. The methodology is illustrated with variable
selection and automatic covariate transformation in the Pima Indians diabetes
data set.Comment: 30 pages, 12 figures, poster contribution at ISBA 201
A new non-parametric detector of univariate outliers for distributions with unbounded support
The purpose of this paper is to construct a new non-parametric detector of
univariate outliers and to study its asymptotic properties. This detector is
based on a Hill's type statistic. It satisfies a unique asymptotic behavior for
a large set of probability distributions with positive unbounded support (for
instance: for the absolute value of Gaussian, Gamma, Weibull, Student or
regular variations distributions). We have illustrated our results by numerical
simulations which show the accuracy of this detector with respect to other
usual univariate outlier detectors (Tukey, MAD or Local Outlier Factor
detectors). The detection of outliers in a database providing the prices of
used cars is also proposed as an application to real-life database
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