By William McCain
ISBN-10: 0878143351
ISBN-13: 9780878143351
This variation expands its scope as a with ease prepared petroleum fluids reference e-book for the training petroleum engineer and an authoritative collage textual content.
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Example text
35 (ej) are normally distributed, their covariance matrix (L;) can be related to the covariance matrix of the measured variables (COK(E yi )=S yi ) through the error propagation law. 38) where the partial derivatives are evaluated at the conditions of the i* experiment. As a result, the elements of the covariance matrix (2^) change from experiment to Copyright © 2001 by Taylor & Francis Group, LLC Formulation of the Parameter Estimation Problem 21 experiment even if we assume that the variance of the measurement error is constant.
Are the degrees of freedom, namely the total number of measurements minus the number of unknown parameters. 32a) or where a is the selected probability level in Fisher's F-distribution and ^Nm-p 's obtained from the F-distribution tables with VI=P and v2=(Nw-p) degrees of freedom. 33) where t ^ / 2 is obtained from the tables of Student's T-distribution with v=Nm-p degrees of freedom. The standard error of parameter k,, c k . 34) Practically, for v>30 we can use the approximation t^ / 2 « zaJ2 where za/2 is obtained from the tables of the standard normal distribution.
Copyright © 2001 by Taylor & Francis Group, LLC Computation of Parameters in Linear Models - Linear Regression Linear models with respect to the parameters represent the simplest case of parameter estimation from a computational point of view because there is no need for iterative computations. Unfortunately, the majority of process models encountered in chemical engineering practice are nonlinear. Linear regression has received considerable attention due to its significance as a tool in a variety of disciplines.
Properties of Petroleum Fluids by William McCain
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