Program for standard statistical distributions

Development of procedure to describe frequency distributions involved in statistical theory is discussed. Representation of frequency distributions by first order differential equation is presented. Classification of various types of distributions based on Pearson parameters is analyzed

Estimating statistical distributions using an integral identity

We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114, (2005)]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method (WHAM). The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function and a joint distribution of amino acid backbone dihedral angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force formula, add discussions to the window size, add extensions to WHAM, and 2d distribution

Generating statistical distributions without maximizing the entropy

We show here how to use pieces of thermodynamics' first law to generate probability distributions for generalized ensembles when only level-population changes are involved. Such microstate occupation modifications, if properly constrained via first law ingredients, can be associated not exclusively to heat and acquire a more general meaning.Comment: 6 pages, no figures, Conferenc

Equilibrium, Adverse Selection, and Statistical Distributions

This paper addresses the problem of multiple equilibria in markets with adverse selection. Akerlof (1970) identified an unique equilibrium of the total market failure under adverse selection. Posterioly, Wilson (1979, 1980) argued that the presence of adverse selection may lead to multiple equilibria. In particular, this paper extends the work of Rose (1993), who stated that the existence of multiple equilibria depends on the distribution of quality. Rose found that multiple equilibria are highly unlikely for most standard probability distributions. This work considers additional statistical distributions for quality. The simulation results suggest the existence of multiple equilibria when the quality follows a beta normal distribution.Adverse Selection; Multiple Equilibria; Statistical Distributions; Akerlof-Wilson Model.

Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system

Power-Law tailed statistical distributions and Lorentz transformations

The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E -\beta \mu$, is the collision invariant, and $\exp_{\kappa}(x)=(\sqrt{1+ \kappa^2 x^2}+\kappa x)^{1/\kappa}$, with $\kappa^2<1$. This, experimentally observed distribution, at low energies behaves as the Maxwell-Boltzmann exponential distribution, while at high energies presents power law tails. Here we show that the function $\exp_{\kappa}(x)$ and its inverse $\ln_{\kappa}(x)$, can be obtained within the one-particle relativistic dynamics, in a very simple and transparent way, without invoking any extra principle or assumption, starting directly from the Lorentz transformations. The achievements support the idea that the power law tailed distributions are enforced by the Lorentz relativistic microscopic dynamics, like in the case of the exponential distribution which follows from the Newton classical microscopic dynamics

Encryption of Covert Information into Multiple Statistical Distributions

A novel strategy to encrypt covert information (code) via unitary projections into the null spaces of ill-conditioned eigenstructures of multiple host statistical distributions, inferred from incomplete constraints, is presented. The host pdf's are inferred using the maximum entropy principle. The projection of the covert information is dependent upon the pdf's of the host statistical distributions. The security of the encryption/decryption strategy is based on the extreme instability of the encoding process. A self-consistent procedure to derive keys for both symmetric and asymmetric cryptography is presented. The advantages of using a multiple pdf model to achieve encryption of covert information are briefly highlighted. Numerical simulations exemplify the efficacy of the model.Comment: 18 pages, 4 figures. Three sentences expanded to emphasize detail. Typos correcte