Student[Statistics] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Packages : Statistics : Student/Statistics/Correlation

Student[Statistics]

  

Correlation

  

compute the correlation

 

Calling Sequence

Parameters

Description

Computation

Examples

References

Compatibility

Calling Sequence

Correlation(X, Y, numeric_option, inert_option)

Correlation(A, B, numeric_option)

Correlation(M, numeric_option)

Parameters

X

-

algebraic; random variable

Y

-

algebraic; random variable

A

-

data sample

B

-

data sample

M

-

Matrix data sample

numeric_option

-

(optional) equation of the form numeric=value where value is true or false

inert_option

-

(optional) equation of the form inert=value where value is true or false

Description

• 

The Correlation function computes the correlation of two data samples or the correlation of multiple data samples in a Matrix.

• 

The first parameter can be a data sample (given as e.g. a Vector), a Matrix data sample, a random variable, or an algebraic expression involving random variables (see Student[Statistics][RandomVariable]).

• 

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

• 

By default, the correlation is computed according to the rules mentioned above. To always compute the correlation numerically, specify the numeric or numeric = true option.

Examples

withStudentStatistics:

Useq57..77

U57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

(1)

Vseqsini,i=57..77

Vsin57,sin58,sin59,sin60,sin61,sin62,sin63,sin64,sin65,sin66,sin67,sin68,sin69,sin70,sin71,sin72,sin73,sin74,sin75,sin76,sin77

(2)

CorrelationU,undefined,V,2

undefined

(3)

CorrelationVectorrow1,2,VectorcolumnPi,2

1π22π212+1π22

(4)

If the computation contains floating point values or the numeric option is included, then a floating point value will be returned.

CorrelationVectorrow1,2.0,VectorcolumnPi,2

−0.999999999566904

(5)

CorrelationVectorrow1,2,VectorcolumnPi,2,numeric

−1.00000000000000

(6)

Compute the correlation between two random variables.

ANormalRandomVariablea,b:

BNormalRandomVariablec,d:

CorrelationA+B,B

ca+c2+d2a+ccb2+d2d

(7)

PNormalRandomVariable2,3:

QNormalRandomVariable1,4:

CorrelationP+Q,Q

45

(8)

Use the inert option.

XPoissonRandomVariable3:

CorrelationX,X,inert

_t=0_t23_tⅇ−3_t!_t0=0_t03_t0ⅇ−3_t0!_t1=0_t13_t1ⅇ−3_t1!_t3=0_t3_t2=0_t23_t2ⅇ−3_t2!23_t3ⅇ−3_t3!_t5=0_t5_t4=0_t43_t4ⅇ−3_t4!23_t5ⅇ−3_t5!

(9)

CorrelationX,X,numeric

0.9999999999

(10)

MMatrix4,2,1,undefined,2.0,4,Pi,4,2

M421undefined2.04π42

(11)

CorrelationM

undefinedFloatundefinedundefinedFloatundefined1.−0.188982236506435undefined−0.1889822365064351

(12)

References

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

• 

The Student[Statistics][Correlation] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

Statistics[Correlation]

Student

Student[Statistics]

Student[Statistics][RandomVariable]