Durbin-Watson parameter

Fluorescence decay profiles are analysed as a sum of up to three exponentials by an iterative reconvolution procedure which has been described elsewhere (17-19) and is based on the Marquardt algoritlim. Goodness of fit is judged by inspection of the weighted residuals, autocorrelation function of the weighted residuals, reduced chi-square value and the Durbin-Watson parameter. 

A = Amplitude, T = Life time and DWP = Durbin Watson Parameter. 

In these equations r is the mean of the weighted residuals. For normally distributed/residuals SK has a mean of zero and a standard deviation of (b/n ). Although we calculate these parameters routinely they are difficult to interpret and therefore we find them less useful than the Durbin-Watson parameter. 

In order to increase the level of confidence, a number of other statistics in addition to xi should be calculated. These include the standard deviation of the wetted residuals, the mean residual, a skewness of fit parameter, and, especially, the Durbin-Watson factor, DB By using DB, calculated according to (57)... 

The analysis involved deconvolution by iterative reconvolution, background subtraction, and optional correction for shift of the instrument response function. Statistical tests included chi-square, the Durbin-Watson test, the covariance matrix, a runs test, and the autocorrelation function [6]. An alternative form of data analysis involves distributions of lifetimes rather than a series of exponentials. Differentiation of systems obeying a decay law made up of three discrete components from systems where there exists a continuous distribution of lifetimes, or a distribution plus one or more discrete components, is a nontrivial analytical problem. Methods involving the minimization of the chi-square parameter are commonly used, but recently the maximum entropy method (MEM) has gained popularity [7]. Inherent in the MEM method is the theoretical lack of bias and the potential for recovering the coefficients of an exponential series with fixed lifetimes which are free of correlation effects and artificial oscillations. Recent work has compared the MEM with a new version of the exponential series method (ESM) which allows use of the same size probe function as the MEM and found that the two methods gave comparable results [8]. 

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