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Computer Contribution 34 (1969)
NONLIN is a FORTRAN IV computer program for estimating parameters in algebraic nonlinear simultaneous equations. The program is designed for problems in which the number of observations equals or exceeds the number of parameters to be estimated. Starting from initial estimates, a modified Gauss-Newton procedure is used to obtain an improved set of parameter values. The process is continued until a set of best estimates has been obtained. A number of options in the program offer wide flexibility in handling a variety of nonlinear problems. Numerical examples are given for dissecting a bimodal distribution into normal components and estimating the porosity in vuggy carbonates.
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Computer Contribution 39 (1969)
Heterogeneity in sample covariance matrices, deriving from differences in the orientation of major axes of the ellipsoids of scatter, may be of common occurrence. The generalized test of equality of covariance matrices will give a significant result in instances where the scatter ellipsoids are (1) unequally inflated, although identically oriented, (2) identically inflated but differently oriented and (3) a combination of these conditions. Equations to the major axes of a scatter ellipsoid of morphologic variables represent growth patterns in the variables. An approximate application of the asymptotic test developed by T. A. Anderson is used here to identify structure of the heterogeneity between two covariance matrices where such exists. The foregoing procedures are preliminary to a treatment of generalized distances in which the path taken by the computer program is decided by structure of the covariance matrices of the samples. Depending on the nature of the covariance matrices either the Mahanolobis' generalized distance is computed or the Anderson-Bahadur distance for heterogeneous covariance matrices. Tests of significance of the results are provided and the linear discriminant function coefficients produced as a by-product.
