TY - JOUR
T1 - Modeling Heavy-Tailed Bounded Data by the Trapezoidal Beta Distribution with Applications
AU - Figueroa-Zu'Niga , Jorge I.
AU - Niklitschek-Soto, Sebastian
AU - Leiva, Víctor
AU - Liu, Shuangzhe
N1 - Funding Information:
The authors thank the editors and reviewers for their constructive comments on an earlier version of this manuscript. The research was partially supported by grant VRID Enlace N.o 217.014.027-1, from the Universidad de Concepción, Chile (J.I. Figueroa-Zúñiga), and by grant FONDECYT 1200525, from the National Agency for Research and Development (ANID) of the Chilean government (V. Leiva).
Publisher Copyright:
© 2022, National Statistical Institute. All rights reserved.
PY - 2022
Y1 - 2022
N2 - In this paper, by using a new method, we derive the trapezoidal beta (TB) distribution and its properties. The TB distribution is a mixture model, generalizes both the beta and rectangu-lar beta distributions, and allows one to describe bounded data with heavy right and/or left tails. In relation to the two-parameter beta distribution, we add two additional parameters which have an intuitive interpretation. The four TB parameters are estimated with the expectation-maximization algorithm. We conduct a simulation study to evaluate performance of the TB distribution. An application with real data is carried out, which includes a comparison among the beta, rectan-gular beta and TB distributions indicating that the TB one describes these data better.
AB - In this paper, by using a new method, we derive the trapezoidal beta (TB) distribution and its properties. The TB distribution is a mixture model, generalizes both the beta and rectangu-lar beta distributions, and allows one to describe bounded data with heavy right and/or left tails. In relation to the two-parameter beta distribution, we add two additional parameters which have an intuitive interpretation. The four TB parameters are estimated with the expectation-maximization algorithm. We conduct a simulation study to evaluate performance of the TB distribution. An application with real data is carried out, which includes a comparison among the beta, rectan-gular beta and TB distributions indicating that the TB one describes these data better.
KW - bounded-support distributions
KW - EM algorithm
KW - mixture distributions
KW - R software
KW - trapezoidal dis-tributions
UR - http://www.scopus.com/inward/record.url?scp=85143619475&partnerID=8YFLogxK
U2 - 10.57805/revstat.v20i3.380
DO - 10.57805/revstat.v20i3.380
M3 - Article
AN - SCOPUS:85143619475
SN - 1645-6726
VL - 20
SP - 387
EP - 404
JO - Revstat Statistical Journal
JF - Revstat Statistical Journal
IS - 3
ER -