부산대학교 도서관

The logistic distribution is generalized using the Marshall-Olkin schemeand its generalization. Some properties are studied. First order autore-gressive time series model with Marshall-Olkin semi-logistic distribution asmarginal is developed and studied.AMS 2000 subject classications.Primary 62E10; Secondary 60E05.Keywords.Autoregressive processes, hazard rate, semi-logistic distribution, stationarity.1. IntroductionLogistic distribution has attracted the attention of many researchers due tothe application of this distribution in various elds. Glasbey (1979) applied thegeneralized logistic curve to the weight gain analysis of Ayshire steer calves,which were recorded weekly from birth to slaughter at 880 ponds. Oliver (1982)applied the logistic curve to human population. Wijesinhaet al.(1983) appliedthe polychotomous logistic regression model to large data set of patients wherethere were many distinct diagnostic categories. Johnson (1985) applied logisticregression to estimate the survival time of diagnosed leukemia patients. Morgan(1985) proposed and applied the cubic logistic model to quantal assay data.By various methods new parameters can be introduced to expand families ofdistributions. Introduction of a scale parameter leads to accelerate life modeland taking powers of a survival function introduces a parameter that leads toproportional hazards model. Marshall and Olkin (1997) introduced a new methodof adding a parameter to expand families of distribution. In particular, startingReceived February 2006; accepted October 2006.1Corresponding author. Department of Statistics, M.D. College, Pazhanji-680542, Thrissurdistrict, Kerala, India (e-mail: ttmathew@redimail.com)