PosRatioDist (version 1.2.1)

f21hyper: f21hyper

Description

Computes the value of a Gaussian hypergeometric function \( F(a,b,c,z) \) for \(-1 \leq z \leq 1\) and \(a,b,c \geq 0\)

Usage

f21hyper(a, b, c, z)

Arguments

a

The parameter a of the Gaussian hypergeometric function, must be a positive scalar here

b

The parameter b of the Gaussian hypergeometric function, must be a positive scalar here

c

The parameter c of the Gaussian hypergeometric function, must be a positive scalar here

z

The parameter z of the Gaussian hypergeometric function, must be between -1 and 1 here

Value

Invalid arguments will return an error message.

Details

The function f21hyper complements the analysis of the 'hyper-g prior' introduced by Liang et al. (2008). For parameter values, compare cf. https://en.wikipedia.org/wiki/Hypergeometric_function#The_series_2F1.

References

Liang F., Paulo R., Molina G., Clyde M., Berger J.(2008): Mixtures of g-priors for Bayesian variable selection. J. Am. Statist. Assoc. 103, p. 410-423

Yuancheng Si and Saralees Nadarajah and Xiaodong Song, (2020). On the distribution of quotient of random variables conditioned to the positive quadrant. Communications in Statistics - Theory and Methods, 49, pp2514-2528.

Saralees Nadarajah and Y.Si (2020) A note on the <U+201C>L-logistic regression models: Prior sensitivity analysis, robustness to outliers and applications<U+201D>. Brazilian Journal of Probability and Statistics,34,p. 183-187.

Examples

# NOT RUN {
f21hyper(30,1,20,.8) #returns about 165.8197
f21hyper(30,10,20,0) #returns one
f21hyper(10,15,20,-0.1) # returns about 0.4872972





# }