log_t function

Log Student's t distribution

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

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

Returns

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.