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).

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`x` |
vector of quantiles. |

`m` |
real number in |

`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.

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