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OwenQ (version 1.0.7)

psbt: Owen distribution functions

Description

Evaluates the Owen cumulative distribution function for an integer number of degrees of freedom.

  • psbt1 evaluates P(T1 ≤ t1, T2 ≤ t2)

  • psbt2 evaluates P(T1 ≤ t1, T2 > t2)

  • psbt3 evaluates P(T1 > t1, T2 > t2)

  • psbt4 evaluates P(T1 > t1, T2 ≤ t2)

Usage

psbt1(nu, t1, t2, delta1, delta2, algo = 2)
psbt2(nu, t1, t2, delta1, delta2, algo = 2)
psbt3(nu, t1, t2, delta1, delta2, algo = 2)
psbt4(nu, t1, t2, delta1, delta2, algo = 2)

Value

A vector of numbers between \(0\) and \(1\), possibly containing some NaN.

Arguments

nu

integer greater than \(1\), the number of degrees of freedom; infinite allowed

t1, t2

two numbers, positive or negative, possibly infinite

delta1, delta2

two vectors of possibly infinite numbers with the same length, the noncentrality parameters

algo

the algorithm used, 1 or 2

References

Owen, D. B. (1965). A special case of a bivariate noncentral t-distribution. Biometrika 52, 437-446.

See Also

It is better to use powen if delta1>delta2.

Examples

Run this code
nu=5; t1=1; t2=2; delta1=2; delta2=3
( p1 <- psbt1(nu, t1, t2, delta1, delta2) )
( p2 <- psbt2(nu, t1, t2, delta1, delta2) )
( p3 <- psbt3(nu, t1, t2, delta1, delta2) )
( p4 <- psbt4(nu, t1, t2, delta1, delta2) )
# the sum should be 1
p1+p2+p3+p4

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