psbt {OwenQ}

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)

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

Value

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

Note

When the number of degrees of freedom is odd, the procedure resorts to the Owen T-function (OwenT).

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

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