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Statistics[HazardRate] - compute the hazard rate

Calling Sequence

HazardRate(X, t, options)

FailureRate(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 hazard rate of a random variable

Description

• 

The HazardRate rate computes the hazard (failure) rate 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 hazard rate is computed using exact arithmetic. To compute the hazard rate numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the hazard rate of the beta distribution with parameters p and q.

HazardRate'Β'p,q,t

&lcub;0t<0t1&plus;p1t1&plus;q&Beta;p&comma;qt<10otherwise1&lcub;0t<0tphypergeomp&comma;1q&comma;1&plus;p&comma;t&Beta;p&comma;qpt<11otherwise

(1)

Use numeric parameters.

HazardRate&apos;&Beta;&apos;3&comma;5&comma;12

105641358hypergeom4&comma;3&comma;4&comma;12

(2)

HazardRate&apos;&Beta;&apos;3&comma;5&comma;12&comma;numeric

7.241379317

(3)

Define new distribution.

T:=DistributionPDF&equals;t&rarr;1&pi;t2&plus;1&colon;

X:=RandomVariableT&colon;

CDFX&comma;t

12&pi;&plus;2arctant&pi;

(4)

FailureRateX&comma;t

1&pi;t2&plus;1112&pi;&plus;2arctant&pi;

(5)

Another distribution

U:=DistributionCDF&equals;t&rarr;Ft&comma;PDF&equals;t&rarr;ft&colon;

Y:=RandomVariableU&colon;

CDFY&comma;t

Ft

(6)

FailureRateY&comma;t

ft1Ft

(7)

See Also

Statistics, Statistics[Computation], Statistics[Distributions], Statistics[RandomVariables]

References

  

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


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