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Statistics

  

Specialize

  

Specialize parameters

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Specialize(X, eqns)

Parameters

X

-

algebraic; random variable or distribution

eqns

-

list of equations, or a single equation, giving values for symbolic parameters in X

Description

• 

The Specialize function takes a random variable or distribution data structure that contains symbolic parameters, and performs a substitution to specialize the given random variable or distribution.

Examples

withStatistics:

Create a random variable which is normally distributed with mean a and standard deviation b.

XRandomVariableNormala,b

X_R

(1)

MeanX,StandardDeviationX

a,b

(2)

By setting a to 0, we obtain a random variable that is normally distributed with mean 0 and standard deviation b.

X1SpecializeX,a=0

X1_R0

(3)

MeanX1,StandardDeviationX1

0,b

(4)

Alternatively, we can set it so that mean and standard deviation are different functions of a single parameter c.

X2SpecializeX,a=c,b=c2

X2_R1

(5)

MeanX2,StandardDeviationX2

c,c2

(6)

Specialize also accepts algebraic expressions involving random variables.

YX+bX2

Y_R1b+_R

(7)

MeanY,StandardDeviationY

bc+a,b2c4+b2

(8)

Y1SpecializeY,b=a

Y1_R1a+_R2

(9)

MeanY1,StandardDeviationY1

ac+a,a2c4+a2

(10)

If a parameter evaluates to a constant, then Maple will complain if that constant does not satisfy the requirements for the parameter. For example, the standard deviation cannot be negative.

SpecializeX,b=1

Error, (in Statistics:-Specialize) invalid parameters obtained when substituting [b = -1]

References

  

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

See Also

Statistics

Statistics[Distribution]

Statistics[MaximumLikelihoodEstimate]

Statistics[RandomVariable]