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 parametersC
and 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。y
is ann
-by-1
vector.
C
is a symmetric, positive definite,d-by-dmatrix, typically a correlation matrix. If its diagonal elements are not 1,mvtcdf
scalesC
to correlation form.mvtcdf
does not rescaleX
。DF
is a scalar, or a vector withnelements.
The multivariatetcumulative probability atX
is 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 byxl
andxu
, respectively.
[y,err] = mvtcdf(...)
returns an estimate of the error iny
。For bivariate and trivariate distributions,mvtcdf
uses 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 ofstatset
parameters are:
'TolFun'
— Maximum absolute error tolerance. Default is1e-8
whend< 4, or1e-4
whend≥ 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
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.