Log Student's t distribution — dlogt • multinma

Density, distribution, and quantile function for the log t distribution, whose logarithm has degrees of freedom df, mean location, and standard deviation scale.

Usage

dlogt(x, df, location = 0, scale = 1)

plogt(q, df, location = 0, scale = 1)

qlogt(p, df, location = 0, scale = 1)

Arguments

x, q: Vector of quantiles
df: Degrees of freedom, greater than zero
location: Location parameter
scale: Scale parameter, greater than zero
p: Vector of probabilities

Value

dlogt() gives the density, plogt() gives the distribution function, qlogt() gives the quantile function.

Details

If \(\log(Y) \sim t_\nu(\mu, \sigma^2)\), then \(Y\) has a log t distribution with location \(\mu\), scale \(\sigma\), and df \(\nu\).

The mean and all higher moments of the log t distribution are undefined or infinite.

If df = 1 then the distribution is a log Cauchy distribution. As df tends to infinity, this approaches a log Normal distribution.