Estimation of parameters in logistic and log-logistic distribution with grouped data |
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Authors: | Yan Yan Zhou Jie Mi Shengru Guo |
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Institution: | (1) Department of Statistics, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA |
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Abstract: | 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. |
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Keywords: | Log-logistic distribution Grouped sample Maximum likelihood estimators Failure rate mode |
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