Distribution inverse Gaussian

Weiss, M., A note on the role of generalized inverse Gaussian distributions of circulatory transit times in pharmacokinetics, Journal of Mathematical Biology, Vol. 20, 1984, pp. 95-102. 

In the assumed inverse-gaussian distribution for the water residence time r, the temporal moments from the TRUE-1 evaluation for the STT-IB tests are used, i.e., the mean residence time is 5 h, and the variance is 1.5 h. The linear relationship between and r is taken as /] = 3000r, i.e., k = 3000 1/m (Cvetkovic et al., 2000). 

The values of temporal moments for the inverse-Gaussian distribution of the water residence time r are chosen based on simple reasoning of scaling. If the flow rate is 1000 time lower, then the mean travel time will be about 1000 time longer. Therefore for Task 6B, a mean residence time of 5000 h is used. The variance for Task 6B is chosen so that the coefficient of variation is the same as that in Task 6A. The variance becomes therefore 1.5x10 h. The proportionality of the linear relationship between P and t is assumed to be same, i.e.,P= iT,k = 3000 1/m. 

Doksum, K. and A. Hoyland (1992). Models for variable-stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution. Technometrics 34(1), 74- 2. 

An early development of the simple molecular network theory is the so-called inverse Langevin approximation for the probability distribution. The Gaussian approximation is... 

Bhattacharyya Fries (1982) pointed out that the product s failure time is the first passage time of the drift Brownian motion to a critical value (threshold), and it follows inverse Gaussian distribution. The corresponding reliability function is... 

Doksum K.A. Hoyland A. 1992. Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution. Technometrics. 1(34) 74-82. 

Smith Ch. E. Lansky P. 1994. A reliability application of a mixture of inverse Gaussian distributions. Applied Stochastic Models and Data Analysis 10 61-69. 

As was shown, the conventional method for data reconciliation is that of weighted least squares, in which the adjustments to the data are weighted by the inverse of the measurement noise covariance matrix so that the model constraints are satisfied. The main assumption of the conventional approach is that the errors follow a normal Gaussian distribution. When this assumption is satisfied, conventional approaches provide unbiased estimates of the plant states. The presence of gross errors violates the assumptions in the conventional approach and makes the results invalid. 

It is noted that both the probability distribution of Eq. (2.16) and the temperature factor of Eq. (2.19) are Gaussian functions, but with inversely related mean-square deviations. Analogous to the relation between direct and reciprocal space, the Fourier transform of a diffuse atom is a compact function in scattering space, and vice versa. 

This filter is not an inverse filter of the type that we seek, being intended only for noise reduction. It does not undo any spreading introduced by s(x). It is, however, an optimum filter in the sense that no better linear filter can be found for noise reduction alone, provided that we are restricted to the knowledge that the noise is additive and Gaussian distributed. 

For a network of Gaussian chains having the same number n of links, uniaxially stretched by an amount L/Lo = A., the assumptions of affine displacement of jimction points and initial Gaussiein distribution of end-to-end vectors allows one to calculate the optical anisotropy of the network by integrating Eq.lO over the distribution of end-to-end vectors in the stretched state. By taking Treloar s expansion [11] for the inverse Langevin function, the orientation distribution function for the network can be put into the form of a power series of the number of Unks per chain ... 

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