Search results for "Normal"
showing 10 items of 2571 documents
The distribution of stock returns: international evidence
1994
Although financial theory rests heavily on the normality assumption, daily stock returns display significant departures from normality. Different researchers have proposed alternative distributions. In this paper, the distribution of stock returns is examined in six stock markets. The empirical distributions present common features and are best represented by Student's t-distribution, while several alternative distributions are rejected.
Estimating Engel curves under unit and item nonresponse
2010
SUMMARY This paper estimates food Engel curves using data from the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE). Our statistical model simultaneously takes into account selectivity due to unit and item nonresponse, endogeneity problems, and issues related to flexible specification of the relationship of interest. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the unobservables in the model follow a multivariate Gaussian distribution, while the semiparametric specification avoids distributional assumptions about the unobservables. Copyright © 2011 John Wiley & Sons, Ltd.
Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance
2009
The main purpose of this paper is to present a theoretically sound portfolio performance measure that takes into account higher moments of the distribution of returns. First, we perform a study of the investor's preferences to higher moments of distribution within expected utility theory and discuss the performance measurement. To illustrate the investor's preferences to higher moments and the computation of a performance measure, we provide an approximation analysis of the optimal capital allocation problem and derive a formula for the Sharpe ratio adjusted for skewness of distribution. This performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges…
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…
Sampling properties of the Bayesian posterior mean with an application to WALS estimation
2022
Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this pa…
On the world distribution of income
2015
In this paper we demonstrate that the size distribution of the world income may be reasonably approximated by a log-normal distribution rather then by a power law, as has previously been believed. This result has been shown to be quite persistent as we move from 1985 to 2011.
Sirenomelia, case report and review of the literature.
2020
We present a case of sirenomelia diagnosed in the first trimester of pregnancy. The ultrasound examination showed fused lower extremities and an anechoic structure in the lower abdomen that is clue in the early diagnosis. The postmortem study showed the existence of a single umbilical artery (vitelline artery), with an origin in the abdominal aorta. This finding not only explained the presence of a vascular steal with subsequent underdeveloped of pelvic organs, but also differentiated this condition from caudal regression syndrome.
Biorthonormal-basis method for the vector description of optical-fiber modes
1998
This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.
Quasi-Normal Frequencies in Open Cavities: An Application to Photonic Crystals
2005
The electromagnetic field in an optical open cavity is analyzed in the framework of the Quasi-Normal Modes theory. The role of the complex quasi-normal frequencies in the transmission coefficient and their link with the density of quasi-modes function is clarified. An application to a quarter-wave symmetric one-dimensional photonic crystals is discussed to illustrate the usefulness and the meaning of our results.
Spectral Analysis of Nonrelativistic Quantum Electrodynamics
2001
I review the research results on spectral properties of atoms and molecules coupled to the quantized electromagnetic field or on simplified models of such systems obtained during the past decade. My main focus is on the results I have obtained in collaboration with Jurg Frohlich and Israel Michael Sigal [8, 9, 10, 11, 12, 13].