Search results for "Gaussian distribution"
showing 10 items of 16 documents
Maximum probability estimators in the case of exponential distribution
1975
In 1966–1969L. Weiss andJ. Wolfowitz developed the theory of „maximum probability” estimators (m.p.e.'s). M.p.e.'s have the property of minimizing the limiting value of the risk (see (2.10).) In the present paper, therfore, after a short description of the new method, a fundamental loss function is introduced, for which—in the so-called regular case—the optimality property of the maximum probability estimators yields the classical result ofR.A. Fisher on the asymptotic efficiency of the maximum likelihood estimator. Thereby it turns out that the m.p.e.'s possess still another important optimality property for this loss function. For the latter the parameters of the exponential distribution—…
Performance of adaptive sample size adjustment with respect to stopping criteria and time of interim analysis
2006
The benefit of adjusting the sample size in clinical trials on the basis of treatment effects observed in interim analysis has been the subject of several recent papers. Different conclusions were drawn about the usefulness of this approach for gaining power or saving sample size, because of differences in trial design and setting. We examined the benefit of sample size adjustment in relation to trial design parameters such as 'time of interim analysis' and 'choice of stopping criteria'. We compared the adaptive weighted inverse normal method with classical group sequential methods for the most common and for optimal stopping criteria in early, half-time and late interim analyses. We found …
A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps
2021
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the CBOE websi…
Dynamic copula models for the spark spread
2011
We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.
Modeling Term Structure Dynamics in the Nordic Electricity Swap Market
2010
We analyze the daily returns of Nordic electricity swaps and identify significant risk premia in the short end of the market. On average, long positions in this part of the swap market yield negative returns. The daily returns are distinctively non-normal in terms of tail-fatness, but we find little evidence of asymmetry. We investigate if the flexible four-parameter class of normal inverse Gaussian (NIG) distributions can capture the observed stylized facts and find that this class of distributions offers a remarkably improved fit relative to the normal distribution. We also compare the fit with that of the four-parameter class of stable distributions; the NIG law outperforms the stable la…
Separate regression modelling of the Gaussian and Exponential components of an EMG response from respiratory physiology.
2014
If Y1 \sim N(\mu ;\sigma^2) and Y2 \sim Exp(\nu), with Y1 independent of Y2, then their sum Y = Y1 +Y2 follows an Exponentially Modified Gaussian (EMG) distribution. In many applications it is of interest to model the two components separately, in order to investigate their (possibly) different important predictors. We show how this can be done through a GAMLSS with EMG response, and apply this separate regression modelling strategy to a dataset on lung function variables from the SAPALDIA cohort study.
Observation and Mass Measurement of the BaryonΞb−
2007
We report the observation and measurement of the mass of the bottom, strange baryon $\Xi^-_b$ through the decay chain $\Xi^-_b \to J/\psi \Xi^-$, where $J/\psi \to \mu^+ \mu^-$, $\Xi^- \to \Lambda \pi^-$, and $\Lambda \to p \pi^-$. Evidence for observation is based on a signal whose probability of arising from the estimated background is 6.6 x 10^{-15}, or 7.7 Gaussian standard deviations. The $\Xi^-_b$ mass is measured to be $5792.9\pm 2.5$ (stat.) $\pm 1.7$ (syst.) MeV/$c^2$.
A Comparison among Portfolio Selection Strategies with Subordinated Lévy Processes
2007
In this paper we describe portfolio selection models using Lévy processes. The contribution consists in comparing some portfolio selection strategies under different distributional assumptions. We first implement portfolio models under the hypothesis the log-returns follow a particular process with independent and stationary increments. Then we compare the ex-post final wealth of optimal portfolio selection models with subordinated Lévy processes when limited short sales and transaction costs are allowed.
Discrete Time Portfolio Selection with Lévy Processes
2007
This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal Inverse Gaussian model or a Brownian Motion. In particular, we propose an ex-ante and an ex-post empirical comparisons by the point of view of different investors. Thus, we compare portfolio strategies considering different term structure scenarios and different distributional assumptions when unlimited short sales are allowed.
On VaR using modified gaussian copula
2008
The problem of modeling asset returns is one of the most important issue in finance. People generally use Gaussian processes because of their tractable properties for computation. However, it is well known that asset returns are fat-tailed leading to an underestimation of the risk. One of the most recent proposals is to model the interdependence of asset returns, for example in a portfolio, by means of Copulas and choose marginal distributions with fat tail to fit the single asset returns. The aim of the paper is to show first results concerning the evaluation of Portfolio Value-at-Risk (VaR) using the Gaussian copula, modified by introducing a particular correlation coefficient, and assumi…