ABSTRACT
The lognormal is a "long-tailed" positively skewed distribution that is an appropriate model in life-span and reaction-time studies where data are often highly skewed. It has been studied extensively by numerous investigators. Among these are Yuan (1933), Cohen (1951, 1976, 1988), Aitchison and Brown (1957), Hill (1963), Johnson and Kotz (1970), Giesbrecht and Kempthorne (1976), Kane (1978, 1982), Cohen et al. (1985), Wingo (1975, 1976), Munro and Wixley (1970), Stedinger (1980), Rukhin (1984), Crow and Shimizu (1988), and many others. Estimation of lognormal parameters from complete samples has been effectively treated by various writers among those referenced here. In this chapter we are primarily concerned with parameter estimation in the three-parameter lognormal distribution from truncated and censored samples. Both modified maximum likelihood estimators, which employ the first-order statistic, and local maximum likelihood estimators are considered. Because of regularity problems to be discussed later, global maximum likelihood estimation is not always feasible.
The lognormal distribution derives its name from the relation it bears to the normal distribution. If the random variable Y = ln(X - 'Y) is normally distributed
