# [R] Define t-distribution using data, and ghyp package

Scott.Wilkinson at csiro.au Scott.Wilkinson at csiro.au
Wed Aug 8 06:42:44 CEST 2007

```Dear R users,

I am fitting a t-distribution to some data, then selecting randomly from
the distribution. I am using the brand new ghyp package, which seems
designed to do this. Firstly is this approach appropriate or are their
alternatives I should also consider? I have a small dataset and the
hyperbolic distribution is also used when heavy tails are expected, but
I understand the t-distribution is designed for understanding variance
when data are limited.

I have 2 questions specific to ghyp; as this package is new perhaps my
limited knowledge is complemented by some teething issues:

1. How should I set argument nu in function fit.tuv()? It appears to be
a starting value. The preliminary draft help file says "nu is defined as
-2*lambda" but lambda is not defined. Experimenting with Data1 below,
nu=2.5 gives no error messages and hist() looks vaguely reasonable,
although >Dist1 lists Converge=FALSE. Nu=2 gives "Error in FUN(newX[,
i], ...) : If lambda < 0: chi must be > 0 and psi must be >= 0! lambda =
-1;   chi = 0;   psi = 0". Nu=3 gives "Warning message: NaNs produced
in: sqrt(diag(hess)), and again >Dist1 gives Converge=FALSE, but also
the resulting hist() is scrambled.

Looking at Data2, again nu=2.5 gives no error messages, and >Dist2 lists
Converge=TRUE. Interestingly, Dist2 lists nu=18.2927194, but if I set
nu=18 in fit.tuv() I get "Warning message: NaNs produced in:
sqrt(diag(hess))", and Converge=FALSE (!).

2. What is the significance/consequence of Converge=FALSE? How can I
achieve Converge=TRUE apart from collecting more data?

3. In fit.tuv() I have experimented with setting argument symmetric=TRUE
but why is the distribution always "Asymmetric Student-t"?

Code:
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library(ghyp)
Data1 <- c(37.07000, 46.94609, 38.19270, 41.98090, 36.45126, 45.25217,
39.07771, 39.35987)
Dist1 <- fit.tuv(Data1, nu = 2.5, opt.pars = c(nu = T, mu = T, sigma =
T), symmetric = T)
hist(Dist1, data = Data1, gaussian = T, log.hist = F, ylim = c(0,0.5),
ghyp.col = 1, ghyp.lwd = 1,
ghyp.lty = "solid", col = 1, nclass = 30)

Data2 <- c(0.07, 2.68, 2.00, 0.27, 0.39, 1.17, 1.34, 4.34, 3.36, 3.61,
1.28)
Dist2 <- fit.tuv(Data2, nu = 2.5, opt.pars = c(nu = T, mu = T, sigma =
T), symmetric = T)
hist(Dist2, data = Data2, gaussian = T, log.hist = F, ylim = c(0,1),
ghyp.col = 1, ghyp.lwd = 1,
ghyp.lty = "solid", col = 1, nclass = 30)
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