... A number of different statistical methods are used for estimating parameters from a data set. The most commonly used one is the least squares method which estimates a parameter by minimizing the function : . where y is the dependent and x the independent variables while f is a given function. ... The most important assumptions are that the errors in the dependent variable are normal distributed, the variance is homogeneous, and the independent variables have no errors and are uncorrelated. ...

Next: Star Formation Rate and Up: No Title Previous: Calculation of Evolutionary Tracks . To start calculations, we choose the distributions of the initial binary parameters: the mass of the primary ZAMS component, , binary mass ratio, , orbital separation a . ... whereas the mass ratio distribution is not. ... The zero assumption often made is that the mass ratio distribution has a flat shape, that is binaries with a high mass ratio occur as frequently as those with equal masses. ...

... Up: Data Analysis Tools, Techniques, and Software . Previous: Starfinder: a Code for Crowded Stellar Fields Analysis . Table of Contents - Subject Index - Author Index - PS reprint - . ... 216, Astronomical Data Analysis Software and Systems IX, eds. N. Manset, C. Veillet, D. Crabtree (San Francisco: ASP), 627 . ... Kitt Peak National Observatory, National Optical Astronomy Observatories, P.O. Box 26732, Tucson, AZ 85726 . ...

Next: Simulations Up: Maximum Likelihood Estimation of Previous: Introduction . The properties of an ensemble of faint galaxies can be defined by the distribution of the parameters of the models that best fit each individual object. ... The model also includes instrumental parameters, such as the sky background (estimated locally) and amplitude of the noise. ... The probability of the observed value is then computed for each pixel using the adopted error distribution. ...

... In brief: the frequency-dependent radiative transfer equation is solved for a dust under assumption of spherically-symmetric geometry for its distribution taking into account particle size distribution and quantum heating effects for the very small dust particles. ... Table: Model parameters for IRAS04296+3429. ... parameter . ... hot dust shell) . ... The best fit to the spectral energy distribution of IRAS04296 is shown by heavy solid line (see Table2 for details concerning parameters of the model...