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.