Functions of statistics

There is also a special subset of statistical techniques that is part of both the second and third functions of statistics. This is data transformation, which includes such things as the conversion of numbers to log or probit values. 

Communication and display of data are the most commonly used function of statistical graphics in toxicology, whether used for internal reports, presentations at meetings, or formal publications in the literature. In communicating data, graphs should not be used to duplicate data that are presented in tables, but rather to show important trends and/or relationships in the data. Though such communication is most commonly of a quantitative compilation of actual data, it can be also be used to... 

Generalize this definition to dots in three dimensions and verify that it is the pair distribution function of statistical mechanics. 

Other ions in the solution. The self-energy of a dipole embedded in a dielectric sphere is the key to Onsager s theory of the dielectric constant of dipolar fluids. Equally, in any theory for, say, the surface energy of water, or adsorption of molecule, the self-energy of a molecule as a function of its distance from an interface is involved. In adsorption proper, the same selfenergy for a molecule appears in the partition function of statistical mechaiucs from which the adsorption isotherm is derived. 

Roe, R. J., Krigbaum, W. R. Orientation distribution function of statistical segments in deformed polymer networks. J. Appl. Phys. 35, 2215 (1964). 

Statistics is a collection of methods of enquiry used to gather, process, or interpret quantitative data. The two main functions of Statistics are to describe and summarize data and to make inferences about a larger population of which the data are representative. These two areas are referred to as Descriptive and Inferential Statistics, respectively both areas have an important part to play in Data Mining. Descriptive Statistics provides a toolkit of methods for data summarization while Inferential Statistics is more concerned with data analysis. 

The generalized gamma distribution is one of the most studied probabihty density functions of statistics since many of the important nondiscrete density functions can be derived from it. For example, /(y (2,0, V2A)) is the one-sided normal distribution, and/(y (l, /2— 1,2)) is the / -distribution. In the special case of = a — 1 the gamma distribution is called a Weibull distribution and in case of a = 1 we obtain the Gamma distribution. 

The transient fluctuation theorem is applied to the transient response of a system. It bridges the microscopic and macroscopic domains and links the time-reversible and irreversible description of processes. In transient fluctuations, the time averages are calculated from a zero time with the known initial distribution function until a finite time. The initial distribution function may be, for example, one of the equilibrium distribution functions of statistical mechanics. So, for arbitrary averaging times, the transient fluctuation theorems are exact. The transient fluctuation theorem describes how irreversible macroscopic behavior evolves from time-reversible microscopic dynamics as either the observation time or the system size increases. It also shows how the entropy production can be related to the forward and backward dynamical randomness of the trajectories or paths of systems as characterized by the entropies per unit time. 

A small error in the computation of the values of the descriptors, compared to the error of the experimental (observed) values of the dependent property, is an important condition for correct functioning of statistical computations. Compared to other descriptors used in QSAR calculations, the topological indices have the advantage that their value is determined with a much smaller error than the value of the biochemical activity. 

To explain the Gibbs paradox and to prove the 11. P.T. we use the concept of bound information (2 15). This method is identical with introducing the Boltzman function of statistical physics. Its negative value, determined by a detailness of our description of an observed system, is proved to be a value of Clausius entropy (in a certain substitute equivalent equilibrium thermod5mamic way (19)). We show that a physical realization of such observation is equivalent to a scheme of a relevant (reversible) heat cycle (7). Its properties are expressible in terms of the Gibbs paradox. 

For a transient double-network at deformation, the distribution functions of statistical conformation for two kinds of chains are obtained after introducing a condition of affine deformatimi, which is shown as follow ... 

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