dsgc: Density function of the square-root generalized conventional...
In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

Density function of the SGC distribution described in the Supplementary Material of Ott et al. (2021).

1	dsgc(x, m, C)

`x`	vector of quantiles.
`m`	real number in (1,∞).
`C`	non-negative real number.

The density function with domain [0, ∞) is given by

π(x) = 2(m-1)Cx(1+Cx^2)^{-m}

for x >= 0. This is the transformation of the density function for variance components given in equation (2.15) in Berger & Deely (1988) to the standard deviation scale. See the Supplementary Material of Ott et al. (2021), Section 2.2, for more information.

For meta-analsis data sets, Ott et al. (2021) choose C=σ_{ref}^{-2}, where σ_{ref} is the reference standard deviation (see function sigma_ref) of the data set, which is defined as the geometric mean of the standard deviations of the individual studies.

Value of the density function at locations x, where x >= 0. Vector of non-negative real numbers.

Berger, J. O., Deely, J. (1988). A Bayesian approach to ranking and selection of related means with alternatives to analysis-of-variance methodology. Journal of the American Statistical Association 83(402), 364–373.

Ott, M., Plummer, M., Roos, M. Supplementary Material: How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Revised for Statistics in Medicine. 2021.

dsigc