The asymmetric bimodal exponential power (ABEP) distribution is an extension of the 8 generalized gamma distribution to the real line via adding two parameters which fit the shape of 9 peakedness in bimodality on real line. The special values of peakedness parameters of the distribution 10 are combination of half Laplace and half normal distributions on real line. The distribution has 11 two pa...

Previous work has shown that it is often essential to account for the variation in rates at different sites in phylogenetic models in order to avoid phylogenetic artifacts such as long branch attraction. In most current models, the gamma distribution is used for the rates-across-sites distributions and is implemented as an equal-probability discrete gamma. In this article, we introduce discrete...

Self-diffusion in polymer solutions studied with pulsed-field gradient nuclear magnetic resonance (PFG NMR) is typically based either on a single self-diffusion coefficient, or a log-normal distribution of self-diffusion coefficients, or in some cases mixtures of these. Experimental data on polyethylene glycol (PEG) solutions and simulations were used to compare a model based on a gamma distrib...

In this paper, a new distribution is introduced by taking the product of the probability density functions of Bessel distribution of second kind and gamma distribution. Some distributional properties and a characterization of the proposed product distribution are provided. The percentile points for some selected values of parameters are also presented. It is hoped that the proposed product dist...

BACKGROUND Posterior mapping is an increasingly popular hierarchical Bayesian based method used to infer character histories and reconstruct ancestral states at nodes of molecular phylogenies, notably of morphological characters. As for all Bayesian analyses specification of prior values is an integrative and important part of the analysis. He we provide an example of how alternative prior choi...

A classical approach to combine independent test statistics is Fisher's combination of $p$-values, which follows the $\chi ^2$ distribution. When the test statistics are dependent, the gamma distribution (GD) is commonly used for the Fisher's combination test (FCT). We propose to use two generalizations of the GD: the generalized and the exponentiated GDs. We study some properties of mis-using ...

Simplifying assumptions made in various tree reconstruction methods--notably rate constancy among nucleotide sites, homogeneity, and stationarity of the substitutional processes--are clearly violated when nucleotide sequences are used to infer distant relationships. Use of tree reconstruction methods based on such oversimplified assumptions can lead to misleading results, as pointed out by prev...

We construct a family of martingales with Gaussian marginal distributions. We give a weak construction as Markov, inhomogeneous in time processes, and compute their infinitesimal generators. We give the predictable quadratic variation and show that the paths are not continuous. The construction uses distributions Gσ having a logconvolution semigroup property. Further, we categorize these proces...

We investigate the properties of multifractal products of the exponential of Ornstein-Uhlenbeck processes driven by Lévy motion. The conditions on the mean, variance and covariance functions of these processes are interpreted in terms of the moment generating functions. We provide an illustrative example of Euler’s gamma distribution. We establish the corresponding log-Euler multifractal scenar...

This paper proposes a statistical steganalysis method for quantization index modulation (QIM) based steganography. We have shown that, in general, plain-quantization (quantization without message embedding) reduces local-randomness (or increases local-correlation) in the resulting quantized-object and QIM-stego exhibits higher level of local-randomness than the corresponding quantized cover. Th...