TY - JOUR
T1 - Generalized logistic distribution and its regression model
AU - Aljarrah, Mohammad A.
AU - Famoye, Felix
AU - Lee, Carl
N1 - Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - A new generalized asymmetric logistic distribution is defined. In some cases, existing three parameter distributions provide poor fit to heavy tailed data sets. The proposed new distribution consists of only three parameters and is shown to fit a much wider range of heavy left and right tailed data when compared with various existing distributions. The new generalized distribution has logistic, maximum and minimum Gumbel distributions as sub-models. Some properties of the new distribution including mode, skewness, kurtosis, hazard function, and moments are studied. We propose the method of maximum likelihood to estimate the parameters and assess the finite sample size performance of the method. A generalized logistic regression model, based on the new distribution, is presented. Logistic-log-logistic regression, Weibull-extreme value regression and log-Fréchet regression are special cases of the generalized logistic regression model. The model is applied to fit failure time of a new insulation technique and the survival of a heart transplant study.
AB - A new generalized asymmetric logistic distribution is defined. In some cases, existing three parameter distributions provide poor fit to heavy tailed data sets. The proposed new distribution consists of only three parameters and is shown to fit a much wider range of heavy left and right tailed data when compared with various existing distributions. The new generalized distribution has logistic, maximum and minimum Gumbel distributions as sub-models. Some properties of the new distribution including mode, skewness, kurtosis, hazard function, and moments are studied. We propose the method of maximum likelihood to estimate the parameters and assess the finite sample size performance of the method. A generalized logistic regression model, based on the new distribution, is presented. Logistic-log-logistic regression, Weibull-extreme value regression and log-Fréchet regression are special cases of the generalized logistic regression model. The model is applied to fit failure time of a new insulation technique and the survival of a heart transplant study.
KW - Beta-family
KW - Censored data
KW - Hazard function
KW - Moments
KW - Symmetric distribution
UR - http://www.scopus.com/inward/record.url?scp=85090246334&partnerID=8YFLogxK
U2 - 10.1186/s40488-020-00107-8
DO - 10.1186/s40488-020-00107-8
M3 - Article
AN - SCOPUS:85090246334
VL - 7
JO - Journal of Statistical Distributions and Applications
JF - Journal of Statistical Distributions and Applications
SN - 2195-5832
IS - 1
M1 - 7
ER -