dsgc | R Documentation |

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

```
dsgc(x, m, C)
```

`x` |
vector of quantiles. |

`m` |
real number in |

`C` |
non-negative real number. |

The density function with domain `[0, \infty)`

is given by

```
\pi(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=\sigma_{ref}^{-2}`

,
where `\sigma_{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. (2021). Supplementary Material:
How vague is vague? How informative is informative? Reference analysis for
Bayesian meta-analysis. *Statistics in Medicine*.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.9076")}

`dsigc`

```
dsgc(x=c(0.1,0.5,1), m=1.2, C=10)
```

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