Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

CiteULike is a free service for managing and discovering scholarly references - click here to get started.

Sign In to gain access to subscriptions and/or personal tools.
Statistical Modelling
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Rigby, R. A
Right arrow Articles by Stasinopoulos, D M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Using the Box-Cox t distribution in GAMLSS to model skewness and kurtosis

Robert A Rigby

STORM Research Centre, London Metropolitan University, UK, r.rigby{at}londonmet.ac.uk

D Mikis Stasinopoulos

STORM Research Centre, London Metropolitan University, UK

The Box-Cox t (BCT) distribution is presented as a model for a dependent variable Y exhibiting both skewness and leptokurtosis. The distribution is defined by a power transformation Y v having a shifted and scaled (truncated) t distribution with degrees of freedom parameter {tau}. The distribution has four parameters and is denoted by BCT(µ, {sigma},{nu}, {tau}). The parameters µ, {sigma},{nu} and {tau} may be interpreted as relating to location (median), scale (centile-based coefficient of variation), skewness (power transformation to symmetry) and kurtosis (degrees of freedom), respectively. The generalized additive model for location, scale and shape (GAMLSS) is extended to allow each of the parameters of the distribution to be modelled as linear and/or non-linear parametric and/or smooth non-parametric functions of explanatory variables. A Fisher scoring algorithm is used to fit the model by maximizing a (penalized) likelihood. The first and expected second and cross derivatives of the likelihood with respect to µ, {sigma},{nu} and {tau}, required for the algorithm, are provided. The use of the BCT distribution is illustrated by two data applications.

Key Words: centile estimation • cubic smoothing splines • generalized additive models • LMS method • non-linear model • penalized likelihood • reference curves • regression quantiles

Statistical Modelling, Vol. 6, No. 3, 209-229 (2006)
DOI: 10.1191/1471082X06st122oa
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?