Student: Student's t Distribution

In QRM: Provides R-Language Code to Examine Quantitative Risk Management Concepts

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") 

Example output

Loading required package: gsl
Loading required package: Matrix
Loading required package: mvtnorm
Loading required package: numDeriv
Loading required package: timeSeries
Loading required package: timeDate

Attaching package: 'QRM'

The following object is masked from 'package:base':

    lbeta

[1] 137.1341 190.6782

QRM documentation built on April 14, 2020, 6:49 p.m.