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Student[Statistics]

  

ProbabilityDensityFunction

  

compute the probability density function

  

PDF

  

compute the probability density function

 

Calling Sequence

Parameters

Description

Computation

Examples

References

Compatibility

Calling Sequence

ProbabilityDensityFunction(X, t, numeric_option, output_option, inert::truefalse:=false)

PDF(X, t, numeric_option, output_option, inert::truefalse:=false)

Parameters

X

-

algebraic; random variable

t

-

algebraic; point

numeric_option

-

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

output_option

-

(optional) equation of the form output=x where x is value, plot, or both

inert_option

-

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

Description

• 

The ProbabilityDensityFunction function computes the probability density function of the specified random variable at the specified point.

• 

The first parameter a random variable, or an algebraic expression involving random variables (see Student[Statistics][RandomVariable]).

• 

If the option output is not included or is specified to be output=value, then the function will return the value of the probability density function of the specified random variable at the specified point. If output=plot is specified, then the function will return a density plot of the input random variable together with dash lines instructing the value at the specified point. If output=both is specified, then both the value and the plot will be returned.

• 

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 the second parameter is a floating point value or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

• 

By default, the PDF of the specified random variable at the specified point is computed according to the rules mentioned above. To always compute the value numerically, specify the numeric or numeric = true option.

Examples

withStudentStatistics:

Compute the probability density function of the beta random variable with parameters p and q.

ProbabilityDensityFunctionBetaRandomVariablep,q,t

0t<0t1+p1t1+qΒp&comma;qt<10otherwise

(1)

Use numeric parameters.

ProbabilityDensityFunctionBetaRandomVariable3&comma;5&comma;12

10564

(2)

ProbabilityDensityFunctionBetaRandomVariable3&comma;5&comma;12&comma;numeric

1.640625000

(3)

Use the output=plot option.

ProbabilityDensityFunctionBetaRandomVariable3&comma;5&comma;12&comma;output&equals;plot

Define new random variable and use the output = both option and the inert option.

AExponentialRandomVariable4&plus;2UniformRandomVariable3&comma;5&plus;1&colon;

pdf&comma;graphPDFA&comma;5&comma;output&equals;both&comma;inert&colon;

PDFA&comma;5&comma;numeric

0.05736968759

(4)

pdf

0_t<0&ExponentialE;_t44otherwise0_t2<−518_t2<30otherwise2&DifferentialD;_t

(5)

evalfpdf

0.05736968759

(6)

graph

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][ProbabilityDensityFunction] and Student[Statistics][PDF] commands were introduced in Maple 18.

• 

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

See Also

Statistics[PDF]

Student

Student[Statistics]

Student[Statistics][RandomVariable]