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MillsRatio

  

compute the Mills ratio

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

Calling Sequence

MillsRatio(X, t, options)

Parameters

X

-

algebraic; random variable or distribution

t

-

algebraic; point

options

-

(optional) equation of the form numeric=value; specifies options for computing the Mills ratio of a random variable

Description

• 

The MillsRatio ratio computes the Mills ratio of the specified random variable at the specified point.

• 

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

Computation

• 

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

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Options

  

The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the Mills ratio is computed using exact arithmetic. To compute the Mills ratio numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the Mills ratio of the beta distribution with parameters p and q.

MillsRatioΒp,q,t

10t<0tphypergeomp&comma;1q&comma;1+p&comma;tΒp&comma;qpt<11otherwise0t<0t1+p1t1+qΒp&comma;qt<10otherwise

(1)

Use numeric parameters.

MillsRatioΒ3&comma;5&comma;12

641058hypergeom−4&comma;3&comma;4&comma;123

(2)

MillsRatioΒ3&comma;5&comma;12&comma;numeric

0.138095238095238

(3)

Define new distribution.

TDistribution`=`PDF&comma;t1πt2+1&colon;

XRandomVariableT&colon;

CDFX&comma;t

π+2arctant2π

(4)

MillsRatioX&comma;t

1π+2arctant2ππt2+1

(5)

Another distribution

UDistribution`=`CDF&comma;tFt&comma;`=`PDF&comma;tft&colon;

YRandomVariableU&colon;

CDFY&comma;t

Ft

(6)

MillsRatioY&comma;t

1Ftft

(7)

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[Computation]

Statistics[Distributions]

Statistics[RandomVariables]