TY - JOUR
T1 - Failure rate of birnbaum–saunders distributions
T2 - Shape, change-point, estimation and robustness
AU - Athayde, Emilia
AU - Azevedo, Assis
AU - Barros, Michelli
AU - Leiva, Víctor
N1 - Funding Information:
The authors thank the Editors and two referees for their constructive comments on an earlier version of this manuscript. Emilia Athayde and Assis Azevedo were partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Fundaçao para a Ciência e a Tecnolo-gia”, through the Project UID/MAT/00013/2013. Michelli Barros was partially supported by the Brazilian Council for Scientific and Technological Development (CNPq in Portuguese). Victor Leiva was partially supported by the Chilean Council for Scientific and Technology Research (Conicyt in Spanish), grant FONDECYT 1160868.
Publisher Copyright:
© Brazilian Statistical Association, 2019.
PY - 2019/5
Y1 - 2019/5
N2 - The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.
AB - The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.
KW - Bootstrapping
KW - Likelihood-based methods
KW - Logistic
KW - Monte Carlo simulation
KW - Normal and Student-t distributions
KW - R computer language
UR - http://www.scopus.com/inward/record.url?scp=85063345417&partnerID=8YFLogxK
U2 - 10.1214/17-BJPS389
DO - 10.1214/17-BJPS389
M3 - Article
AN - SCOPUS:85063345417
VL - 33
SP - 301
EP - 328
JO - Brazilian Journal of Probability and Statistics
JF - Brazilian Journal of Probability and Statistics
SN - 0103-0752
IS - 2
ER -