bayesmeta (version 3.4)

dhalflogistic: Half-logistic distribution.

Description

Half-logistic density, distribution, and quantile functions, random number generation and expectation and variance.

Usage

dhalflogistic(x, scale=1, log=FALSE)
  phalflogistic(q, scale=1)
  qhalflogistic(p, scale=1)
  rhalflogistic(n, scale=1)
  ehalflogistic(scale=1)
  vhalflogistic(scale=1)

Value

‘dhalflogistic()’ gives the density function,

‘phalflogistic()’ gives the cumulative distribution function (CDF),

‘qhalflogistic()’ gives the quantile function (inverse CDF), and ‘rhalflogistic()’ generates random deviates. The ‘ehalflogistic()’ and ‘vhalflogistic()’

functions return the corresponding half-logistic distribution's expectation and variance, respectively.

Arguments

x, q

quantile.

p

probability.

n

number of observations.

scale

scale parameter (\(>0\)).

log

logical; if TRUE, logarithmic density will be returned.

Author

Christian Roever

Details

The half-logistic distribution is simply a zero-mean logistic distribution that is restricted to take only positive values. If \(X\sim\mathrm{logistic}\), then \(|sX|\sim\mathrm{halflogistic}(\mathrm{scale}\!=\!s)\).

References

C. Roever, R. Bender, S. Dias, C.H. Schmid, H. Schmidli, S. Sturtz, S. Weber, T. Friede. On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis. Research Synthesis Methods, 12(4):448-474, 2021. tools:::Rd_expr_doi("10.1002/jrsm.1475").

N.L. Johnson, S. Kotz, N. Balakrishnan. Continuous univariate distributions, volume 2, chapter 23.11. Wiley, New York, 2nd edition, 1994.

See Also

dlogis, dhalfnormal, dlomax, drayleigh, TurnerEtAlPrior, RhodesEtAlPrior, bayesmeta.

Examples

#######################
# illustrate densities:
x <- seq(0,6,le=200)
plot(x, dhalfnormal(x), type="l", col="red", ylim=c(0,1),
     xlab=expression(tau), ylab=expression("probability density "*f(tau)))
lines(x, dhalflogistic(x), col="green3")
lines(x, dhalfcauchy(x), col="blue")
lines(x, dexp(x), col="cyan")
abline(h=0, v=0, col="grey")

# show log-densities (note the differing tail behaviour):
plot(x, dhalfnormal(x), type="l", col="red", ylim=c(0.001,1), log="y",
     xlab=expression(tau), ylab=expression("probability density "*f(tau)))
lines(x, dhalflogistic(x), col="green3")
lines(x, dhalfcauchy(x), col="blue")
lines(x, dexp(x), col="cyan")
abline(v=0, col="grey")