fit.mle.t: Fit a T Distribution via Maximum Likelihood Estimation

In christopherggreen/cggmisc: Christopher G Green's Miscellaneous Functions

Description

Fits a location-scale model based on Student's t distribution using maximum likelihood estimation.

Usage

fit.mle.t(obsvals, mean.exists = TRUE, na.rm = FALSE, verbose = FALSE)

Arguments

obsvals	A vector of observations.
mean.exists	Should it be assumed that the underlying T distribution has a finite first moment (i.e., that nu > 1)? By default it is assumed that nu > 1, and this condition is enforced in the fitting process.
na.rm	If TRUE, missing values in obsvals are removed prior to fitting the distribution. Note: the fitting process will likely fail if your data contains missing values and you use na.rm = FALSE.
verbose	If TRUE, diagnostics are printed during the fitting process. Useful for debugging.

Details

fit.mle.t fits a location-scale model based on Student's t distribution using maximum likelihood estimation. The distributional model in use here assumes that the random variable X follows a location-scale model based on the Student's t distribution; that is,

(X - mu)/(sigma) ~ T_{nu},

where mu and sigma are location and scale parameters, respectively, and nu is the degrees of freedom parameter of the T distribution. fit.mle.t uses the likelihood and score functions provided by likelihood.t and score.t.

Value

df	Estimated degrees of freedom parameter nu
mu	Estimated location parameter mu
sigma	Estimated scale parameter sigma

Author(s)

Christopher G. Green [e-mail]

References

The likelihood and score functions used were calculated as part of one of the author's qualifying exams. See Chapter 3 of the paper below.

Green, C. G. (2005) Heavy-Tailed Distributions in Finance: An Empirical Study. Qualifying Exam, Department of Statitics, University of Washington. Available from http://students.washington.edu/cggreen/uwstat/papers/computing_prelim_2005_green.pdf

More general calculations for the information matrix of general multivariate elliptic distributions can be found in the work of Ann F. S. Mitchell.

Mitchell, Ann F. S. (1989) The Information Matrix, Skewness Tensor and alpha-Connections for the General Multivariate Elliptic Distribution. Annals of the Institute for Statistics and Math, 41 (2), pp 289-304.

See Also

likelihood.t, score.t

There are several other packages that offer functions to fit the Student's t and related distributions using other approaches.

• The MASS package contains the fitdistr function, which can fit many univariate distributions via maximum likelihood.

• The PearsonDS package fits general Pearson distributions, of which the Student's t distribution is a special case;

• The GeneralizedHyperbolic package fits the generalized hyperbolic distribution, of which the Student's t distribution is a special case.

• The SkewHyperbolic package fits the skew hyperbolic distribution, of which the skewed t distribution is a special case.

• The fGarch package fits the Student's t distribution via the stdFit function.

• The function tFit in the fBasics package fits the Student's t distribution.

Examples

a <- -5 + 2*rt(1000, df=4)
fit.mle.t(a)

christopherggreen/cggmisc documentation built on May 13, 2019, 7:04 p.m.