help drawnorm dialog: drawnorm
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Title
[D] drawnorm -- Draw sample from multivariate normal distribution
Syntax
drawnorm newvarlist [, options]
options description
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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
Also see
Manual: [D] drawnorm
Help: [D] corr2data, [R] set seed
