TY - JOUR
T1 - Multivariate failure time distributions derived from shared frailty and copulas
AU - Wang, Yin Chen
AU - Emura, Takeshi
N1 - Publisher Copyright:
© 2021, Japanese Federation of Statistical Science Associations.
PY - 2021/12
Y1 - 2021/12
N2 - Copulas and frailty models have been two major tools for modeling dependence in multivariate failure time distributions. The objective of this paper is to investigate multivariate failure time models that include copula models and frailty models as special cases. To this end, we revisit a broad family of multivariate failure time models proposed by Marshall and Olkin (JASA 83:834–841, 1988). This family accommodates both frailty and copulas, unlike the models that accommodate only one of them. However, their work focused on very specific copulas and is limited to bivariate models. Instead, we focus more on popular members of copulas and some multivariate models. Another novel feature of our paper is to restrict our attention to the shared frailty model, and call our restricted class as the generic name “frailty-copula”. This name yields a taxonomic classification of all the members of distributions. We also consider somewhat complex frailty distributions (two-parameter gamma, lognormal, truncated-normal, and folded-normal), which were not considered in Marshall and Olkin (1988) and other papers of frailty models. To illustrate the usefulness of the proposed model, we briefly discuss maximum likelihood estimation methods with some numerical evaluations.
AB - Copulas and frailty models have been two major tools for modeling dependence in multivariate failure time distributions. The objective of this paper is to investigate multivariate failure time models that include copula models and frailty models as special cases. To this end, we revisit a broad family of multivariate failure time models proposed by Marshall and Olkin (JASA 83:834–841, 1988). This family accommodates both frailty and copulas, unlike the models that accommodate only one of them. However, their work focused on very specific copulas and is limited to bivariate models. Instead, we focus more on popular members of copulas and some multivariate models. Another novel feature of our paper is to restrict our attention to the shared frailty model, and call our restricted class as the generic name “frailty-copula”. This name yields a taxonomic classification of all the members of distributions. We also consider somewhat complex frailty distributions (two-parameter gamma, lognormal, truncated-normal, and folded-normal), which were not considered in Marshall and Olkin (1988) and other papers of frailty models. To illustrate the usefulness of the proposed model, we briefly discuss maximum likelihood estimation methods with some numerical evaluations.
KW - Bivariate distribution
KW - Copula
KW - FGM copula
KW - Frailty
KW - Reliability
KW - Survival analysis
UR - http://www.scopus.com/inward/record.url?scp=85108839397&partnerID=8YFLogxK
U2 - 10.1007/s42081-021-00123-1
DO - 10.1007/s42081-021-00123-1
M3 - 文章
AN - SCOPUS:85108839397
SN - 2520-8764
VL - 4
SP - 1105
EP - 1131
JO - Japanese Journal of Statistics and Data Science
JF - Japanese Journal of Statistics and Data Science
IS - 2
ER -