Distribution finite mixture

Everitt, B.S. and Hand, D.J. (1981). Finite mixture distributions. Chapman and Hall, New York. 

Finite mixture distributions may be valuable when a distribution appears to result from mixing of somewhat distinct subpopulations, e.g., if there appear to be multiple modes in a distribution. 

Everitt, B.S. An introduction to finite mixture distributions. Statistical Methods in Medical Research 1996 5 107-127. 

Diebolt, X, and Robert, C.R (1994). Estimation of Finite Mixture Distributions through Bayesian Sampling. Journal of the Royal Statistical Society, Series B, 56, 363-375. 

In our hands,photolysis of ort/to-cyanophenyl azide in the presence of diethylamine gives 5//-azepine trapping products, 13c and 14c (Scheme 3). Variation of the solvent led to subtle variation in the product distribution. The solvent effect on the relative rates of cyclization towards and away from the cyano group is small, but finite. The compositions of the mixtures formed under different reaction conditions are shown in Table 5. 

A more detailed study of fuel cloud dispersion, though one lacking direct exptl verification, was made by Rosenblatt et al (Ref 23). The purpose of their study was to develop and use physically based numerical simulation models to examine the cloud dispersion and cloud detonation with fuel mass densities and particle size distributions as well as the induced air pressures and velocities as the principal parameters of interest. A finite difference 2-D Eulerian code was used. We quote The basic numerical code used for the FAE analysis was DICE, a 2-D implicit Eulerian finite difference technique which treats fluid-particle mixtures. DICE treats par-... 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

The Arrhenius form of the reaction results from the Maxwell speed distribution and the rate at which molecular bonds in gas-phase species are broken [44], In full-scale fire modeling, the finite reaction rates must be considered if one attempts to model things such as CO and soot production and oxidation, or ignition and extinction. However, then the simple mixture fraction formulation must be supplemented by additional variables keeping track of the reaction progress. 

Step 2 Estimation by the Fenske equation [Eq. (14.1)] of the distribution, dA>, of the nonkey components between distillate and bottoms at total reflux using the value of computed in Step 1, the b/d ratio for the heavy key, and the relative volatility between the nonkey and the heavy key, aNK,HK- Although this estimate is for total reflux conditions, it is a surprisingly good estimate for the distribution of the nonkey components at finite reflux conditions for nearly ideal mixtures. 

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