Student {QRM}

Student's t Distribution

Description

Functions for evaluating density, fitting and random variates of multivaraite Student's t distribution and routines for quantiles and fitting of univariate distribution.

Usage

dmt(x, df, mu, Sigma, log = FALSE)
rmt(n, df = 4, mu = 0, Sigma)
qst(p, mu = 0, sd = 1, df, scale = FALSE)
fit.st(data, ...)
fit.mst(data, nit = 2000, tol = 1e-10, ...)

Arguments

x

matrix, dimension n \times d; density is evaluated for each row.

df

numeric, degrees of freedom.

mu

numeric, location parameters.

Sigma

matrix, dispersion matrix.

log

logical, returning log density values.

data

numeric, data used for uni- and multivariate fitting.

nit

integer, number of iterations of EM-type algorithm.

tol

numeric, tolerance of improvement for stopping iteration.

p

numeric, probability.

sd

numeric, scale parameters.

scale

logical, scaling Student's t distribution.

n

integer, count of random variates.

...

ellipsis, arguments are passed down to optim() in fit.st() and to MCECMupdate() in fit.mst().

See Also

link{EMupdate}, link{MCECMupdate}, and link{MCECM.Qfunc}

Examples

BiDensPlot(func = dmt, xpts = c(-4, 4), ypts = c(-4, 4), mu = c(0, 0),
           Sigma = equicorr(2, -0.7), df = 4)
## Quantiles of univariate Student's t
p <- c(0.90,0.95)
s <- 0.2 * 10000/sqrt(250)
qst(p, sd = s, df = 4, scale = TRUE)
## Fitting multivariate Student's t
Sigma <- diag(c(3, 4, 5)) %*% equicorr(3, 0.6) %*% diag(c(3, 4, 5)) 
mu <- c(1, 2 ,3) 
tdata <- rmt(1000, 4, mu = mu, Sigma = Sigma) 
mod1 <- fit.mst(tdata, method = "BFGS")
## DJ data
data(DJ)
r <- returns(DJ)
s <- window(r[, "MSFT"], "1993-01-01", "2000-12-31")
mod.t1 <- fit.st(100 * s)
stocks <- c("AXP","EK","BA","C","KO","MSFT",
            "HWP","INTC","JPM","DIS")
ss <- window(r[, stocks], "1993-01-01", "2000-12-31")
fridays <- time(ss)[isWeekday(time(ss), wday = 5)]
ssw <- aggregate(ss, by = fridays, FUN = sum)
mod.t2 <- fit.mst(ssw, method = "BFGS")