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Title
[D] drawnorm -- Draw sample from multivariate normal distribution
Syntax
drawnorm newvarlist [, options]
options Description
---------------------------------------------------------------------------------------------
Main
clear replace the current dataset
double generate variable type as double; default is float
n(#) # of observations to be generated; default is current number
sds(vector) standard deviations of generated variables
corr(matrix|vector) correlation matrix
cov(matrix|vector) covariance matrix
cstorage(full) correlation/covariance structure is stored as a symmetric k*k matrix
cstorage(lower) correlation/covariance structure is stored as a lower triangular
matrix
cstorage(upper) correlation/covariance structure is stored as an upper triangular
matrix
forcepsd force the covariance/correlation matrix to be positive semidefinite
means(vector) means of generated variables; default is means(0)
Options
seed(#) seed for random-number generator
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Menu
Data > Create or change data > Other variable-creation commands > Draw sample from normal
distribution
Description
drawnorm draws a sample from a multivariate normal distribution with desired means and
covariance matrix. The default is orthogonal data with mean 0 and variance 1. The
covariance matrix may be singular. The values generated are a function of the current
random-number seed or the number specified with set seed(); see [R] set seed.
Options
+------+
----+ Main +---------------------------------------------------------------------------------
clear specifies that the dataset in memory be replaced, even though the current dataset has
not been saved on disk.
double specifies that the new variables be stored as Stata doubles, meaning 8-byte reals. If
double is not specified, variables are stored as floats, meaning 4-byte reals. See [D]
data types.
n(#) specifies the number of observations to be generated. The default is the current number
of observations. If n(#) is not specified or is the same as the current number of
observations, drawnorm adds the new variables to the existing dataset; otherwise,
drawnorm replaces the data in memory.
sds(vector) specifies the standard deviations of the generated variables. sds() may not be
specified with cov().
corr(matrix|vector) specifies the correlation matrix. If neither corr() nor cov() is
specified, the default is orthogonal data.
cov(matrix|vector) specifies the covariance matrix. If neither cov() nor corr() is
specified, the default is orthogonal data.
cstorage(full|lower|upper) specifies the storage mode for the correlation or covariance
structure in corr() or cov(). The following storage modes are supported:
full specifies that the correlation or covariance structure is stored (recorded) as a
symmetric k*k matrix.
lower specifies that the correlation or covariance structure is recorded as a lower
triangular matrix. With k variables, the matrix should have k(k+1)/2 elements in the
following order:
C(11) C(21) C(22) C(31) C(32) C(33) ... C(k1) C(k2) ... C(kk)
upper specifies that the correlation or covariance structure is recorded as an upper
triangular matrix. With k variables, the matrix should have k(k+1)/2 elements in the
following order:
C(11) C(12) C(13) ... C(1k) C(22) C(23) ... C(2k) ... C(k-1k-1) C(k-1k) C(kk)
Specifying cstorage(full) is optional if the matrix is square. cstorage(lower) or
cstorage(upper) is required for the vectorized storage methods. See storage modes for
examples.
forcepsd modifies the matrix C to be positive semidefinite (psd), and so be a proper
covariance matrix. If C is not positive semidefinite, it will have negative eigenvalues.
By setting negative eigenvalues to 0 and reconstructing, we obtain the least-squares
positive-semidefinite approximation to C. This approximation is a singular covariance
matrix.
means(vector) specifies the means of the generated variables. The default is means(0).
+---------+
----+ Options +------------------------------------------------------------------------------
seed(#) specifies the initial value of the random-number seed used by the runiform()
function. The default is the current random-number seed. Specifying seed(#) is the same
as typing set seed # before issuing the drawnorm command.
Examples
Generate 2000 independent observations (x,y); x with mean 2 and standard deviation .5; y with
mean 3 and standard deviation 2.
. matrix m = (2,3)
. matrix sd = (.5,2)
. drawnorm x y, n(2000) means(m) sds(sd)
. summarize
Draw a sample of 1000 observations from a bivariate standard normal distribution, with
correlation 0.5.
. clear
. matrix C = (1, .5 \ .5, 1)
. drawnorm x y, n(1000) corr(C)
. summarize
Equivalently,
. clear
. matrix C = (1, .5, 1)
. drawnorm x y, n(1000) corr(C) cstorage(lower)
. summarize
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