TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 157

SAS/Ets User's Guide 157. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 1552 F Chapter 22 The SEVERITY Procedure Experimental If the method used to compute the EDF is any method other than the STANDARD method then the statistic can be computed by using the following two pieces of information The EDF estimate is a step function. In the interval Z - _1 Z - it is equal to Fn Zi _j . Using the probability integral transform z F y the formula simplifies to 1 Fn z - z 2 AD N A dz -i z 1 - z The computation formula can then be derived from the following approximation AD N X z i 1 Zi-1 F Zz_i - z 2 ----f dz z 1 - z Assuming Z0 0 Z 1 1 Fn 0 0 and Fn Zn 1 yields the following computation formula AD -N - N log 1 - Zi - N log ZN N N X Fn Zi-1 2Bi - Fn Zi-1 - 1 2Ci i 2 where B log Z - log Z -i and C log 1 - Z - log 1 - Z -i . CvM The Cramer-von-Mises CvM statistic is a quadratic EDF statistic that is proportional to the expected value of the squared difference between the EDF and CDF. It is formally defined as follows CvM N 1 1 F y - F y 2dF y If the STANDARD method is used to compute the EDF then the following formula is used CvM Zi - r y 12N 2N i 1 v 7 If the method used to compute the EDF is any method other than the STANDARD method then the statistic can be computed by using the following two pieces of information The EDF estimate is a step function. In the interval Z _1 Z it is equal to _i . Using the probability integral transform z F y the formula simplifies to CvM D N C Fn z 1 z 2dz The computation formula can then be derived from the following approximation N 1 z CvM N X Fn Zi-1 - z 2dz i 1 z -1 Output Data Sets F 1553 Assuming Z0 0 Zn i 1 and Fn 0 0 yields the following computation formula CvM N N X Fn Zi-i 2 Zi - Zi-i - Fn Zi- Zf - Z i 2 This formula is similar to the one proposed by Koziol and Green 1976 . Output Data Sets PROC SEVERITY writes OUTEST OUTSTAT OUTCDF and OUTMODELINFO data sets when requested with respective options. The data sets and their contents are described in the following sections. OUTEST Data Set The OUTEST .

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