Functions for evaluating density, fitting and random variates of
multivaraite Student's t distribution and routines for quantiles and
fitting of univariate distribution.
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")
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(QRM)
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
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/QRM/Student.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Student
> ### Title: Student's t Distribution
> ### Aliases: Student dmt rmt qst fit.st fit.mst
> ### Keywords: distribution
>
> ### ** 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)
[1] 137.1341 190.6782
> ## 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")
>
>
>
>
>
> dev.off()
null device
1
>
providing 
.