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mvtcdf

Multivariatetcumulative distribution function

Syntax

y = mvtcdf(X,C,DF)
y = mvtcdf(xl,xu,C,DF)
[y,err] = mvtcdf(...)
[...] = mvntdf(...,options)

Description

y = mvtcdf(X,C,DF)returns the cumulative probability of the multivariatetdistribution with correlation parametersCand degrees of freedomDF,在每一行评估X。Rows of then-by-dmatrixX对应于观测值或点,列对应于变量或坐标。yis ann-by-1vector.

Cis a symmetric, positive definite,d-by-dmatrix, typically a correlation matrix. If its diagonal elements are not 1,mvtcdfscalesCto correlation form.mvtcdfdoes not rescaleXDFis a scalar, or a vector withnelements.

The multivariatetcumulative probability atXis defined as the probability that a random vectorT, distributed as multivariatet, will fall within the semi-infinite rectangle with upper limits defined byX, i.e.,Pr{T(1)X(1),T(2)X(2),...T(d)X(d)}

y = mvtcdf(xl,xu,C,DF)返回多元tcumulative probability evaluated over the rectangle with lower and upper limits defined byxlandxu, respectively.

[y,err] = mvtcdf(...)returns an estimate of the error iny。For bivariate and trivariate distributions,mvtcdfuses adaptive quadrature on a transformation of thetdensity, based on methods developed by Genz, as described in the references. The default absolute error tolerance for these cases is1e-8。对于四个或多个维度,mvtcdf如参考文献中所述,使用基于Genz和Bretz开发的方法基于Genz和Bretz开发的方法。这些情况的默认绝对错误公差是1e-4

[...] = mvntdf(...,options)specifies control parameters for the numerical integration used to computey。This argument can be created by a call tostatset。Choices ofstatsetparameters are:

  • 'TolFun'— Maximum absolute error tolerance. Default is1e-8whend< 4, or1e-4whend≥ 4.

  • 'MaxFunEvals'— Maximum number of integrand evaluations allowed whend≥ 4. Default is1e7'MaxFunEvals'is ignored whend< 4.

  • 'Display'— Level of display output. Choices are'off'(the default),'iter', and'final''Display'is ignored whend< 4.

Examples

collapse all

计算多变量的CDFtdistribution with correlation parametersC = [1 .4; .4 1]and 2 degrees of freedom.

C = [1 .4; .4 1]; df = 2; [X1,X2] = meshgrid(linspace(-2,2,25)',linspace(-2,2,25)'); X = [X1(:) X2(:)]; p = mvtcdf(X,C,df);

Plot the cdf.

figure; surf(X1,X2,reshape(p,25,25));

参考

[1] Genz, A. “Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities.”Statistics and Computing。Vol. 14, No. 3, 2004, pp. 251–260.

[2] Genz, A., and F. Bretz. “Numerical Computation of Multivariate t Probabilities with Application to Power Calculation of Multiple Contrasts.”Journal of Statistical Computation and Simulation。Vol. 63, 1999, pp. 361–378.

[3] Genz,A。和F. Bretz。“比较多元T概率计算方法的方法。”计算和图形统计杂志。Vol. 11, No. 4, 2002, pp. 950–971.

Introduced in R2006a