Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Spontaneous Interblink Time Distributions in Patients with Graves` Orbitopathy and Normal Subjects

PURPOSE. To determine the shape of spontaneous interblink time interval distributions obtained in a long observation period in normal subjects and patients with Graves` orbitopathy. METHODS. The magnetic search coil technique was used to register the spontaneous blinking activity during 1 hour of video observation of two groups of 10 subjects each (normal controls aged 27-61 years, mean +/- SD = 46.0 +/- 13.6; patients with Graves` orbitopathy aged 33-61 years, mean +/- SD +/- 46.7 +/- 8.9). The spontaneous blink rate of each subject was calculated for the entire period of observation and for 56 five-minute bins. Histograms of the interblink time interval were plotted for each measurement of blink rate. RESULTS. Neither the overall mean blink rate (controls, 19.8 +/- 4.9; Graves`, 17.6 +/- 5.4) nor the interblink time (controls, 5.2 +/- 3.1, Graves`, 7.9 +/- 3.5) differed between the two groups. There was a large variation of both measurements when the 5-minute bins were considered. The interblink time distribution of all subjects was highly positively skewed when the 1-hour period was measured. A significant number of the 5-minute bin distributions deviated from the overall pattern and became symmetric. CONCLUSIONS. The normal blinking process is characterized by highly positively skewed interblink time distributions. This result means that most blinks have a short time interval, and occasionally a small number of blinks have long time intervals. The different patterns of distribution described in the early literature probably represent artifacts because of the small samples analyzed. (Invest Ophthalmol Vis Sci. 2011;52:3419-3424) DOI:10.1167/iovs.10-7060

Drosophila melanogaster lipins are tissue-regulated and developmentally regulated and present specific subcellular distributions

Lipins constitute a novel family of Mg2+-dependent phosphatidate phosphatases that catalyze the dephosphorylation of phosphatidic acid to yield diacylglycerol, an important intermediate in lipid metabolism and cell signaling. Whereas a single lipin is detected in less complex organisms, in mammals there are distinct lipin isoforms and paralogs that are differentially expressed among tissues. Compatible with organism tissue complexity, we show that the single Drosophila Lpin1 ortholog (CG8709, here named DmLpin) expresses at least three isoforms (DmLpinA, DmLpinK and DmLpinJ) in a temporal and spatially regulated manner. The highest levels of lipin in the fat body, where DmLpinA and DmLpinK are expressed, correlate with the highest levels of triacylglycerol (TAG) measured in this tissue. DmLpinK is the most abundant isoform in the central nervous system, where TAG levels are significantly lower than in the fat body. In the testis, where TAG levels are even lower, DmLpinJ is the predominant isoform. Together, these data suggest that DmLpinA might be the isoform that is mainly involved in TAG production, and that DmLpinK and DmLpinJ could perform other cellular functions. In addition, we demonstrate by immunofluorescence that lipins are most strongly labeled in the perinuclear region of the fat body and ventral ganglion cells. In visceral muscles of the larval midgut and adult testis, lipins present a sarcomeric distribution. In the ovary chamber, the lipin signal is concentrated in the internal rim of the ring canal. These specific subcellular localizations of the Drosophila lipins provide the basis for future investigations on putative novel cellular functions of this protein family.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fitting mixtures of Kent distributions to aid in joint set identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planer can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to lit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.