Estimation of parameters in logistic and log-logistic distribution with grouped data

• Published in: Lifetime data analysis Vol. 13; no. 3; pp. 421 - 429
• Main Authors: Zhou, Yan Yan, Mi, Jie, Guo, Shengru
• Format: Journal Article
• Language: English
• Published: United States Springer Nature B.V 01.09.2007
• Subjects: Computer Simulation; Data analysis; Failure analysis; Likelihood Functions; Logistic Models; Logistics; Mathematical models; Random variables; Sample size; Simulation; Studies
• ISSN: 1380-7870; 1572-9249
• DOI: 10.1007/s10985-007-9038-0

In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study.