Histograms general

The histograms in Figure 8 show the distribution of vitrinoids in both the seams. Both the histograms generally show the same type of distribution with a peak of Vc, V4, and Vs on either side of the tail. The mean maximum reflectance values for each zone are presented in Table IV. 

The purpose of statistical evaluation of sample data is to extrapolate from a collection of individual events (e.g., 30 min of process time) to the entire population of events (e.g., 8-h shift). Because microbial monitoring data usually measure the impact of human activity, which is not reproducible exactly from one event to the next, results usually do not fit standard statistical models for normal distributions. In spite of this limitation, it is necessary to summarize the data for comparison to limits. The best statistical methods of evaluation are determined by the nature of the data. Wilson suggests that microbial monitoring data histograms generally resemble Poisson or negative... 

When the underlying distribution is not known, tools such as histograms, probability curves, piecewise polynomial approximations, and general techniques are available to fit distributions to data. It may be necessary to assume an appropriate distribution in order to obtain the relevant parameters. Any assumptions made should be supported by manufacturer s data or data from the literature on similar items working in similar environments. Experience indicates that some probability distributions are more appropriate in certain situations than others. What follows is a brief overview on their applications in different environments. A more rigorous discussion of the statistics involved is provided in the CPQRA Guidelines. ... 

A number of textbooks and review articles are available which provide background and more-general simulation techniques for fluids, beyond the calculations of the present chapter. In particular, the book by Frenkel and Smit [1] has comprehensive coverage of molecular simulation methods for fluids, with some emphasis on algorithms for phase-equilibrium calculations. General review articles on simulation methods and their applications - e.g., [2-6] - are also available. Sections 10.2 and 10.3 of the present chapter were adapted from [6]. The present chapter also reviews examples of the recently developed flat-histogram approaches described in Chap. 3 when applied to phase equilibria. 

The raw curves for //, i and /.to as well as a composite curve formed by shifting data for the two runs by the amount indicated by the arrows are shown in Fig. 10.3. The combined curve provides information over the combined range of particle numbers, N, covered by the two runs. Note that by keeping one-dimensional histograms for N we are restricted to combining runs of the same temperature, while the more general form (10.14) allows combination of runs at different temperatures. 

In the sections below, we describe several studies in which flat-histogram methods were used to examine phase equilibria in model systems. The discussion assumes the reader is familiar with this general family of techniques and the theory behind them, so it may be useful to consult the material in Chap. 3 for background reference. Although the examples provided here entail specific studies, their general form and the principles behind them serve as useful templates for using flat-histogram methods in novel phase equilibria calculations. 

Histograms are graphs of simple frequency distribution. Commonly, the abscissa is the variable of interest (such as lifespan or litter size), and is generally shown as classes or intervals or measurements (such as age ranges of 0 to 10, 10 to 20, weeks, etc.). The ordinate, meanwhile, is the incidence or frequency of observations. The... 

---