The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. In recent years, various methods for comparing the means of two independent log-normal distributions have been developed. In this paper a higher-order likelihoodbased method is proposed. The method is applied to two real-life examples and simulation studies are used compare the accura...

In describing the first-order properties of laser speckle under polarized illumination conditions, it is almost an article of faith that the contrast is unity. In many processing schemes, however, the contrast defined as the quotient of the standard deviation and the mean is calculated over a localized spatial region. In such cases, this local contrast displays a distribution of values that can...

This paper attempts to assess the Europe-wide systemic risk potential in banking. We employ a bivariate GARCH model to estimate conditional correlations between European bank stock indices. These correlations are used as an indication for the interdependencies amongst the banking business and hence for the systemic risk potential. We employ several tests to assess the development of the systemi...

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving limit theorems resulting in non-Gaussian, scale-invariant diffusions. We apply the generalized characteristic functions in combination with a martingale const...

How to test the effect of density estimation methods is the key problem in the statistics. This paper presents a new criterion for assessing the effect of density estimation to select the suitable density estimation method, using the maximum-entropy non-Gaussian measurement. Comparing withχ2-test and Dn-test, the method avoids the problem of the data interval division, and it is suitable for an...

[This corrects the article DOI: 10.1186/s40064-016-2868-z.].

We analyze a sample of bright long bursts and find that the pulses duration have a lognormal distribution while the intervals between pulses have an excess of long intervals (relative to lognormal distribution). This excess can be explained by the existence of quiescent times, long periods with no signal above the background. The lognormal distribution of the intervals (excluding the quiescent ...

The results of R dynamical random surface model (2-dimensional quantum gravity with a R term) are applied to explain the personal income distribution. A scale invariance exists if there is not the R term in the action. The R term provides a typical scale and breaks the scale invariance explicitly in the low and middle income range. A new distribution, Weibull distribution, is deduced from the a...

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic syst...

This paper deals with the challenge of physically displaying reflectance, i.e., the appearance of a surface and its variation with the observer position and the illuminating environment. This is commonly described by the bidirectional reflectance distribution function (BRDF). We provide a catalogue of criteria for the display of BRDFs, and sketch a few orthogonal approaches to solving the probl...