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MULTIVARIATE T CDFName:
The CDF is the integral of the probability density function from negative infinity to the desired value. In addition to the CDF case, this command can handle integration from the specified point to positive infinity and integration from negative infinity to positive infinity. For the multivariate case, you need to specify a varible containing the location estimates for each variable, the variance-covariance matrix of the the variables, a parameter defining the degrees of freedom, and variables specifying the limits of integration. This command uses codes provided by Alan Genz (see the Reference seciton below). In particular, this code supports three different methods:
By default, Dataplot uses the SADMVN method, but you specify one of the other methods (see the Note section below).
where <sigma> is a matrix containing the desired variance-covariance matrix; <nu> is a number or parameter that specifies the desired degrees of freedom for the t distribution; <upplim> is a variable containing the upper levels of integration; and where <par> is a parameter containing the computed multivariate t cdf value. This syntax computes the cdf function.
where <sigma> is a matrix containing the desired variance-covariance matrix; <nu> is a number or parameter that specifies the desired degrees of freedom for the t distribution; <lowlim> is a variable containing the lower levels of integration; <upplim> is a variable containing the upper levels of integration; and where <par> is a parameter containing the computed multivariate t cdf value. This syntax can be used to compute arbitrary integrals of the multivariate t function.
READ MATRIX SIGMA 1 0.5 0.5 0.5 1 0.5 0.5 0.5 1 END OF DATA LET LOWLIM = DATA 1.5 2 0.5 LET A = MULTIVARIATE T CDF SIGMA NU LOWLIM
where <method> is one of the following:
LET RELEPS = <value> These define the desired absolute and relative errors, respectively. The default absolute error is set to 0 and the default relative error is set to 0.005 (i.e., the relative error is used). This should be a reasonable choice for most applications.
"Numerical Computation of Multivariate Normal Probabilities", Alan Genz, Journal of Computational and Graphical Statistics, 1, 1992, pp. 141-149.
let abseps = 0.0 let releps = 0.005 read matrix sigma 1.0 0.75 0.75 0.75 0.75 0.75 1.0 0.75 0.75 0.75 0.75 0.75 1.0 0.75 0.75 0.75 0.75 0.75 1.0 0.75 0.75 0.75 0.75 0.75 1.0 end of data . let cpumin = -infinity let lowl = data cpumin cpumin cpumin cpumin cpumin let uppl = data 2 2 2 2 2 . let nu = 10 let a = multivariate t cdf sigma nu lowl uppl let nu = 20 let a = multivariate t cdf sigma nu lowl uppl let nu = 30 let a = multivariate t cdf sigma nu lowl uppl let nu = 40 let a = multivariate t cdf sigma nu lowl uppl . set multivariate normal kromvt let nu=10 let a = multivariate t cdf sigma nu lowl uppl let nu=20 let a = multivariate t cdf sigma nu lowl uppl let nu=30 let a = multivariate t cdf sigma nu lowl uppl let nu=40 let a = multivariate t cdf sigma nu lowl uppl . set multivariate normal ranmvt let nu=10 let a = multivariate t cdf sigma nu lowl uppl let nu=20 let a = multivariate t cdf sigma nu lowl uppl let nu=30 let a = multivariate t cdf sigma nu lowl uppl let nu=40 let a = multivariate t cdf sigma nu lowl upplDataplot generated the following output ******************* ** let nu = 10 ** ******************* THE COMPUTED VALUE OF THE CONSTANT NU = 0.1000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.90810883E+00 ******************* ** let nu = 20 ** ******************* THE COMPUTED VALUE OF THE CONSTANT NU = 0.2000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92174983E+00 ******************* ** let nu = 30 ** ******************* THE COMPUTED VALUE OF THE CONSTANT NU = 0.3000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92641902E+00 ******************* ** let nu = 40 ** ******************* THE COMPUTED VALUE OF THE CONSTANT NU = 0.4000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92877501E+00 ********* ** . ** ********* ************************************** ** set multivariate normal kromvt ** ************************************** THE FORTRAN COMMON CHARACTER VARIABLE MULTNORM HAS JUST BEEN SET TO KROM ***************** ** let nu=10 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.1000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.90869933E+00 ***************** ** let nu=20 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.2000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92239201E+00 ***************** ** let nu=30 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.3000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92682952E+00 ***************** ** let nu=40 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.4000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92917287E+00 ********* ** . ** ********* ************************************** ** set multivariate normal ranmvt ** ************************************** THE FORTRAN COMMON CHARACTER VARIABLE MULTNORM HAS JUST BEEN SET TO RANM ***************** ** let nu=10 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.1000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.91197872E+00 ***************** ** let nu=20 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.2000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92616749E+00 ***************** ** let nu=30 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.3000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92844337E+00 ***************** ** let nu=40 ** ***************** THE COMPUTED VALUE OF THE CONSTANT NU = 0.4000000E+02 ***************************************************** ** let a = multivariate t cdf sigma nu lowl uppl ** ***************************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.92901456E+00
Date created: 5/21/2003 |