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Chapter26: Statistics
625
Withtheoptionalargumentalt,thealternativeofinterestcanbeselected. Ifaltis
"!="or"<>",thenullhypothesisistestedagainst thetwo-sidedalternativePROB
(x < < y) != 1/2. . If f alt t is s ">",the one-sidedalternative PROB (x x > > y) > 1/2 ("x
is stochastically greater than y") ) is s considered. . Similarly y for r "<", , the e one-sided
alternativePROB(x>y)<1/2("xisstochasticallylessthany")isconsidered. The
defaultisthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, t, df] = t_test
(
x
,
m
,
alt
)
Forasamplexfromanormaldistributionwithunknownmeanandvariance,perform
at-testofthenullhypothesismean(x)==m.
Underthenull,theteststatistict follows aStudentdistributionwith h df=length
(x)-1degreesoffreedom.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis"!="or"<>",thenullistestedagainstthetwo-sidedalternativemean(x)!=m.
Ifaltis">",theone-sidedalternativemean(x)>misconsidered. Similarlyfor"<",
the one-sidedalternative mean(x)<m is considered. . The e default is the two-sided
case.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, t, df] = t_test_2
(
x
,
y
,
alt
)
Fortwosamplesxandyfromnormaldistributionswithunknownmeansandunknown
equalvariances,performatwo-samplet-testofthenullhypothesisofequalmeans.
Underthenull,theteststatistictfollowsaStudentdistributionwithdf degreesof
freedom.
With the optionalargument t string alt, , thealternative of interest t can n be selected.
Ifalt is"!="or"<>",thenullistestedagainst thetwo-sidedalternative mean(x)
!=mean(y). If f alt is ">", the one-sidedalternative mean(x)>mean(y)is used.
Similarlyfor"<",theone-sidedalternativemean(x)<mean(y)isused. Thedefault
isthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, t, df] = t_test_regression
(
y
,
x
,
rr
,
r
,
alt
)
Perform at t testfor the nullhypothesis rr*b=rina classicalnormalregression
modely=x*b+e.
Underthenull,theteststatistictfollowsatdistributionwithdf degreesoffreedom.
Ifr isomitted,avalueof0isassumed.
With the optionalargument t string alt, , thealternative of interest t can n be selected.
Ifaltis "!="or"<>",thenullis testedagainstthetwo-sidedalternative rr*b!=
r. Ifaltis s ">",theone-sidedalternative rr*b>r isused. . Similarly y for "<",the
one-sidedalternativerr*b<risused. Thedefaultisthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
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626
GNUOctave
[FunctionFile]
[pval, z] = = u_test
(
x
,
y
,
alt
)
For two samples x x andy, performa a Mann-Whitney U-test of the null hypothesis
PROB(x>y)==1/2==PROB(x <y).
Underthenull,theteststatisticzapproximatelyfollowsastandardnormaldistribu-
tion. NotethatthistestisequivalenttotheWilcoxonrank-sumtest.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis "!=" or"<>",thenullistestedagainstthetwo-sidedalternativePROB(x >
y)!=1/2.Ifaltis">",theone-sidedalternativePROB(x>y)>1/2isconsidered.
Similarlyfor"<",theone-sidedalternativePROB(x >y)<1/2isconsidered. . The
defaultisthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, f, df_num, df_den] = = var_test
(
x
,
y
,
alt
)
Fortwosamplesxandyfromnormaldistributionswithunknownmeansandunknown
variances,performanF-testofthenullhypothesisofequalvariances.
Underthenull,theteststatisticf followsanF-distributionwithdf
numanddf
den
degreesoffreedom.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis"!="or"<>",thenullistestedagainstthetwo-sidedalternativevar(x)!=var
(y). Ifaltis">",theone-sidedalternativevar(x)>var(y)isused. Similarlyfor
"<",theone-sidedalternativevar(x)>var(y)isused.Thedefaultisthetwo-sided
case.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, t, df] = welch_test
(
x
,
y
,
alt
)
Fortwosamplesxandyfromnormaldistributionswithunknownmeansandunknown
andnot necessarily equalvariances,performaWelchtest ofthe nullhypothesis of
equalmeans.
Underthenull,theteststatistictapproximatelyfollowsaStudentdistributionwith
df degreesoffreedom.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis"!="or"<>",thenullistestedagainstthetwo-sidedalternativemean(x)!=m.
Ifaltis">",theone-sidedalternativemean(x)>misconsidered. Similarlyfor"<",
the one-sidedalternative mean(x) < mis considered. . Thedefault t is the two-sided
case.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, z] = = wilcoxon_test
(
x
,
y
,
alt
)
Fortwomatched-pairsamplevectorsx andy,performaWilcoxonsigned-ranktest
ofthenullhypothesisPROB(x>y)==1/2.
Underthenull,theteststatisticzapproximatelyfollowsastandardnormaldistribu-
tionwhenn>25.
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Chapter26: Statistics
627
Caution: Thisfunctionassumesanormaldistributionforzandthusisinvalidforn
25.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis "!=" or"<>",thenullistestedagainstthetwo-sidedalternativePROB(x >
y)!=1/2.Ifaltis">",theone-sidedalternativePROB(x>y)>1/2isconsidered.
Similarlyfor"<",theone-sidedalternativePROB(x >y)<1/2isconsidered. . The
defaultisthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayed.
[FunctionFile]
[pval, z] = = z_test
(
x
,
m
,
v
,
alt
)
PerformaZ-testofthenullhypothesismean(x)==mforasamplex fromanormal
distributionwithunknownmeanandknownvariancev.
Underthenull,theteststatisticzfollowsastandardnormaldistribution.
Withtheoptionalargumentstringalt,thealternativeofinterestcanbeselected. If
altis"!="or"<>",thenullistestedagainstthetwo-sidedalternativemean(x)!=m.
Ifaltis">",theone-sidedalternativemean(x)>misconsidered. Similarlyfor"<",
the one-sidedalternative mean(x)<m is considered. . The e default is the two-sided
case.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayedalongwithsome
information.
[FunctionFile]
[pval, z] = = z_test_2
(
x
,
y
,
v_x
,
v_y
,
alt
)
Fortwosamplesx andyfromnormaldistributionswithunknownmeansandknown
variancesv
x andv
y,performaZ-testofthehypothesisofequalmeans.
Underthenull,theteststatisticzfollowsastandardnormaldistribution.
With the optionalargument t string alt, , thealternative of interest t can n be selected.
Ifalt is"!="or"<>",thenullistestedagainst thetwo-sidedalternative mean(x)
!=mean(y). If f alt is ">", theone-sided alternative mean(x)>mean(y) is used.
Similarlyfor"<",theone-sidedalternativemean(x)<mean(y)isused. Thedefault
isthetwo-sidedcase.
Thep-valueofthetestisreturnedinpval.
Ifnooutputargumentisgiven,thep-valueofthetestisdisplayedalongwithsome
information.
26.7 RandomNumberGeneration
Octavecangeneraterandomnumbersfromalargenumber ofdistributions. . Therandom
number generators arebasedontherandomnumber generators describedinSection16.3
[SpecialUtilityMatrices],page418.
Thefollowingtablesummarizestheavailablerandomnumbergenerators(inalphabetical
order).
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628
GNUOctave
Distribution
Function
betarnd
BinomialDistribution
binornd
CauchyDistribution
cauchy
rnd
Chi-SquareDistribution
chi2rnd
UnivariateDiscreteDistribution
discrete
rnd
EmpiricalDistribution
empirical
rnd
ExponentialDistribution
exprnd
FDistribution
frnd
gamrnd
GeometricDistribution
geornd
HypergeometricDistribution
hygernd
LaplaceDistribution
laplace
rnd
LogisticDistribution
logistic
rnd
Log-NormalDistribution
lognrnd
PascalDistribution
nbinrnd
UnivariateNormalDistribution
normrnd
PoissonDistribution
poissrnd
StandardNormalDistribution
stdnormal
rnd
t(Student)Distribution
trnd
UnivariateDiscreteDistribution
unidrnd
UniformDistribution
unifrnd
WeibullDistribution
wblrnd
WienerProcess
wienrnd
[FunctionFile]
betarnd
(
a
,
b
)
[FunctionFile]
betarnd
(
a
,
b
,
r
)
[FunctionFile]
betarnd
(
a
,
b
,
r
,
c
,...)
[FunctionFile]
betarnd
(
a
,
b
,
[sz]
)
Returna matrix of random samples fromthe Beta distributionwithparameters s a
andb.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofaandb.
[FunctionFile]
binornd
(
n
,
p
)
[FunctionFile]
binornd
(
n
,
p
,
r
)
[FunctionFile]
binornd
(
n
,
p
,
r
,
c
,...)
[FunctionFile]
binornd
(
n
,
p
,
[sz]
)
Returnamatrixofrandomsamplesfromthebinomialdistributionwithparameters
nandp,wherenisthenumberoftrialsandpistheprobabilityofsuccess.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
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Chapter26: Statistics
629
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofnandp.
[FunctionFile]
cauchy_rnd
(
location
,
scale
)
[FunctionFile]
cauchy_rnd
(
location
,
scale
,
r
)
[FunctionFile]
cauchy_rnd
(
location
,
scale
,
r
,
c
,...)
[FunctionFile]
cauchy_rnd
(
location
,
scale
,
[sz]
)
Returnamatrixofrandomsamples fromtheCauchydistributionwithparameters
locationandscale.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeoflocation
andscale.
[FunctionFile]
chi2rnd
(
n
)
[FunctionFile]
chi2rnd
(
n
,
r
)
[FunctionFile]
chi2rnd
(
n
,
r
,
c
,...)
[FunctionFile]
chi2rnd
(
n
,
[sz]
)
Returnamatrixofrandomsamplesfromthechi-squaredistributionwithndegrees
offreedom.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeofn.
[FunctionFile]
discrete_rnd
(
v
,
p
)
[FunctionFile]
discrete_rnd
(
v
,
p
,
r
)
[FunctionFile]
discrete_rnd
(
v
,
p
,
r
,
c
,...)
[FunctionFile]
discrete_rnd
(
v
,
p
,
[sz]
)
Returnamatrixofrandomsamplesfromtheunivariatedistributionwhichassumes
thevaluesinv withprobabilitiesp.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofv andp.
[FunctionFile]
empirical_rnd
(
data
)
[FunctionFile]
empirical_rnd
(
data
,
r
)
[FunctionFile]
empirical_rnd
(
data
,
r
,
c
,...)
[FunctionFile]
empirical_rnd
(
data
,
[sz]
)
Returnamatrix of randomsamples fromtheempiricaldistributionobtainedfrom
theunivariatesampledata.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
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630
GNUOctave
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifno size arguments are giventhentheresult matrix is a randomorderingofthe
sampledata.
[FunctionFile]
exprnd
(
lambda
)
[FunctionFile]
exprnd
(
lambda
,
r
)
[FunctionFile]
exprnd
(
lambda
,
r
,
c
,...)
[FunctionFile]
exprnd
(
lambda
,
[sz]
)
Return a matrix x of random m samples from the exponential distribution with mean
lambda.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeoflambda.
[FunctionFile]
frnd
(
m
,
n
)
[FunctionFile]
frnd
(
m
,
n
,
r
)
[FunctionFile]
frnd
(
m
,
n
,
r
,
c
,...)
[FunctionFile]
frnd
(
m
,
n
,
[sz]
)
ReturnamatrixofrandomsamplesfromtheFdistributionwithmandndegreesof
freedom.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofmandn.
[FunctionFile]
gamrnd
(
a
,
b
)
[FunctionFile]
gamrnd
(
a
,
b
,
r
)
[FunctionFile]
gamrnd
(
a
,
b
,
r
,
c
,...)
[FunctionFile]
gamrnd
(
a
,
b
,
[sz]
)
eteraandscaleb.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofaandb.
[FunctionFile]
geornd
(
p
)
[FunctionFile]
geornd
(
p
,
r
)
[FunctionFile]
geornd
(
p
,
r
,
c
,...)
[FunctionFile]
geornd
(
p
,
[sz]
)
Returnamatrixofrandomsamplesfromthegeometricdistributionwithparameter
p.
Chapter26: Statistics
631
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeofp.
Thegeometric distributionmodelsthenumberoffailures (x-1)ofaBernoullitrial
withprobabilitypbeforetheﬁrstsuccess(x).
[FunctionFile]
hygernd
(
t
,
m
,
n
)
[FunctionFile]
hygernd
(
t
,
m
,
n
,
r
)
[FunctionFile]
hygernd
(
t
,
m
,
n
,
r
,
c
,...)
[FunctionFile]
hygernd
(
t
,
m
,
n
,
[sz]
)
Returnamatrixofrandomsamples fromthehypergeometricdistributionwithpa-
rameterst,m,andn.
Theparameterst,m,andnmustbepositiveintegerswithmandnnotgreaterthan
t.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeoft,m,and
n.
[FunctionFile]
laplace_rnd
(
r
)
[FunctionFile]
laplace_rnd
(
r
,
c
,...)
[FunctionFile]
laplace_rnd
(
[sz]
)
ReturnamatrixofrandomsamplesfromtheLaplacedistribution.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
[FunctionFile]
logistic_rnd
(
r
)
[FunctionFile]
logistic_rnd
(
r
,
c
,...)
[FunctionFile]
logistic_rnd
(
[sz]
)
Returnamatrixofrandomsamplesfromthelogisticdistribution.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
[FunctionFile]
lognrnd
(
mu
,
sigma
)
[FunctionFile]
lognrnd
(
mu
,
sigma
,
r
)
[FunctionFile]
lognrnd
(
mu
,
sigma
,
r
,
c
,...)
[FunctionFile]
lognrnd
(
mu
,
sigma
,
[sz]
)
Returnamatrixofrandomsamplesfromthelognormaldistributionwithparameters
muandsigma.
632
GNUOctave
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeof muand
sigma.
[FunctionFile]
nbinrnd
(
n
,
p
)
[FunctionFile]
nbinrnd
(
n
,
p
,
r
)
[FunctionFile]
nbinrnd
(
n
,
p
,
r
,
c
,...)
[FunctionFile]
nbinrnd
(
n
,
p
,
[sz]
)
Return a matrix of randomsamples s from m the negative binomialdistributionwith
parametersnandp.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofnandp.
[FunctionFile]
normrnd
(
mu
,
sigma
)
[FunctionFile]
normrnd
(
mu
,
sigma
,
r
)
[FunctionFile]
normrnd
(
mu
,
sigma
,
r
,
c
,...)
[FunctionFile]
normrnd
(
mu
,
sigma
,
[sz]
)
Returnamatrix ofrandomsamplesfromthenormal l distributionwithparameters
meanmuandstandarddeviationsigma.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeof muand
sigma.
[FunctionFile]
poissrnd
(
lambda
)
[FunctionFile]
poissrnd
(
lambda
,
r
)
[FunctionFile]
poissrnd
(
lambda
,
r
,
c
,...)
[FunctionFile]
poissrnd
(
lambda
,
[sz]
)
Returna matrixofrandomsamples from the Poisson distributionwithparameter
lambda.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeoflambda.
[FunctionFile]
stdnormal_rnd
(
r
)
[FunctionFile]
stdnormal_rnd
(
r
,
c
,...)
Chapter26: Statistics
633
[FunctionFile]
stdnormal_rnd
(
[sz]
)
Returnamatrixofrandomsamplesfromthestandardnormaldistribution(mean=
0,standarddeviation=1).
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
[FunctionFile]
trnd
(
n
)
[FunctionFile]
trnd
(
n
,
r
)
[FunctionFile]
trnd
(
n
,
r
,
c
,...)
[FunctionFile]
trnd
(
n
,
[sz]
)
Returnamatrixofrandomsamplesfromthet(Student)distributionwithndegrees
offreedom.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeofn.
[FunctionFile]
unidrnd
(
n
)
[FunctionFile]
unidrnd
(
n
,
r
)
[FunctionFile]
unidrnd
(
n
,
r
,
c
,...)
[FunctionFile]
unidrnd
(
n
,
[sz]
)
Return a matrix x of random m samples from the discrete uniform distribution which
assumestheintegervalues1–nwithequalprobability.
nmaybeascalaroramulti-dimensionalarray.
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthesizeofn.
[FunctionFile]
unifrnd
(
a
,
b
)
[FunctionFile]
unifrnd
(
a
,
b
,
r
)
[FunctionFile]
unifrnd
(
a
,
b
,
r
,
c
,...)
[FunctionFile]
unifrnd
(
a
,
b
,
[sz]
)
Returnamatrixofrandomsamplesfromtheuniformdistributionon[a,b].
Whencalledwithasinglesizeargument,returnasquarematrixwiththedimension
speciﬁed.Whencalledwithmorethanonescalarargumenttheﬁrsttwoargumentsare
matrixdimensions. Thesizemayalsobespeciﬁedwithavectorofdimensionssz.
Ifnosizeargumentsaregiventhentheresultmatrixisthecommonsizeofaandb.
[FunctionFile]
wblrnd
(
scale
,
shape
)
[FunctionFile]
wblrnd
(
scale
,
shape
,
r
)