Statistical moment theory applications

It can readily be seen from this example that the contributions of the extrapolated areas to the total areas are relatively more important for the higher order moments. In this example, the contributions are 28, 61 and 72% for AUC, AUMC and AUSC, respectively. Because of this effect, the applicability of the statistical moment theory is somewhat limited by the precision with which plasma concentrations can be observed. The method also requires a careful design of the sampling process, such that both the peak and the downslope of the curve are sufficiently covered. 

P.R. Mayer and R.K. Brazell, Application of statistical moment theory to pharmacokinetics. J. Clin. Pharmacology, 28 (1988) 481-483. 

Riegelman S, Collier P. The application of statistical moment theory to the evaluation of in vivo dissolution time and absorption time. J Pharmacokinet Biopharm 1980 8 509-534. 

Unfortunately, most of the correlation efforts to date with IR dosage forms have been based on the correlation Level C approach, although there also have been some efforts employing statistical moment theory (Level B). Level A correlation approach is often difficult with IR dosage forms because of the need to sample intensively in the absorptive region of the in vivo study. Thus, Levels B and C are the most practical approaches for IR dosage forms, even though they are not as information-rich and therefore more limited in their application. 

Kakutani, T., Yamaoka, K., Hashida, M. and Sezaki, H. (1985) A new method for assessment of drug disposition in muscle application of statistical moment theory to local perfusion systems. J. Pharmacokin. Biopharm., 13, 609-631. 

Heim and Olejnik [1-3,9] proposed a simple mathematical model based on the theory of statistical moments, whose applicability was confirmed by the results of laboratory-scale studies. 

In recent years, non-compartmental or model-independent approaches to pharmacokinetic data analysis have been increasingly utilized since this approach permits the analysis of data without the use of a specific compartment model. Consequently, sophisticated, and often complex, computational methods are not required. The statistical or non-compartmental concept was first reported by Yamaoka in a general manner and by Cutler with specific application to mean absorption time. Riegelman and Collier reviewed and clarified these concepts and applied statistical moment theory to the evaluation of in vivo absorption time. This concept has many additional significant applications in pharmacokinetic calculations. 

The application of noncompartmental analysis to concentrationtime profiles to calculate primary pharmacokinetic parameters is based on statistical moment theory. - The relationships defined by this approach are valid under the assumption that the system is linear (i.e., net exposure is directly proportional to dose) and parameters are time-invariant. For simplicity, we make an additional assumption that drug is introduced and irreversibly removed only from a single accessible pool (e.g., plasma space). The temporal profile of plasma concentrations, Cp(f), represents a statistical distribution curve, and as such, the zeroth and first statistical moments (Mq and Mi) are defined as ... 

Studies on the application of the theory of statistical moments in the description of grinding in ball mills have been carried out in the Department of Process Equipment, Lodz Technical University [1-3]. The research was carried out in a laboratory scale for selected mineral materials. Results obtained confirmed applicability of the theory of statistical moments in the description of particle size distribution during grinding. 

Dette, H. Studden, W. J. 1997 The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis. New York (NY) John Wiley and Sons. 

The theory and application of statistical moment rest on the tenet that the movement of individual drug molecules through a body compartment is governed by probability. The residence time of a molecule of drug in the body, therefore, can be regarded as a random statistical variable. The mean and the variance of the retention times of a mass of drug molecules reflect the overall behavior of these drug molecules in the... 

In order to compare various reacting-flow models, it is necessary to present them all in the same conceptual framework. In this book, a statistical approach based on the one-point, one-time joint probability density function (PDF) has been chosen as the common theoretical framework. A similar approach can be taken to describe turbulent flows (Pope 2000). This choice was made due to the fact that nearly all CFD models currently in use for turbulent reacting flows can be expressed in terms of quantities derived from a joint PDF (e.g., low-order moments, conditional moments, conditional PDF, etc.). Ample introductory material on PDF methods is provided for readers unfamiliar with the subject area. Additional discussion on the application of PDF methods in turbulence can be found in Pope (2000). Some previous exposure to engineering statistics or elementary probability theory should suffice for understanding most of the material presented in this book. 

A statistical evaluation and comparison of solvatochromic methods used to determine excited-state dipole moments has been carried out by Koutek [167]. Solvent effects can be taken into consideration using the reaction field theory developed by Katritzky, Zemer, Szafran, and Karelson [176-179] and Siretskii, Kirillov, and Bakhshiev [180] have proposed an equation containing a cos where is the angle between the direction of the ground-state dipole moment and the excited-state dipole moment. The equation worked well for certain aromatic dyes but its general applicability has not been tested. 

Density functional theory (DFT) as applied to adsorption is a classical statistical mechanic technique. For a discussion of DFT and classical statistical mechanics, with specific applications to surface problems, the text book by Davis [1] is highly recommended. (Here the more commonly used symbol for number density p(r) is used. Davis uses n(r) so one will have to make an adjustment for this text.) The calculations at the moment may be useful for modeling but are questionable for analysis with unknown surfaces. The reason for this is that the specific forces, or input parameters, required for a calculation are dependent upon the atoms assumed to be present on the surface. For unknown surfaces, a reversion to the use of the Brunaver, Emmett and Teller (BET) equation is often employed. 

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