Two-Parameter Lognormal Distribution

Abstract

The logarithmic normal probability law is widely used to describe the distribution of annual maximum values of hourly or daily precipitation (Weiss, 1957), flood flows (Chow, 1951, 1954), hydraulic conductivity (Freeze and Cherry, 1979), soil properties (physical, chemical and microbiological) (Parkin and Robinson, 1993), etc. Kalinske (1946) found that many times river discharge data and sand sizes followed the normal law if they were logarithmically transformed. Chow (1951, 1954, 1959) gave a historical background of the log-probability law and discussed its wide-ranging application in engineering, and exensively worked with the lognormal distribution. Aitchison and Brown (1957) presented a comprehensive statistical treatment of the lognormal distribution. Parkin et al. (1988) evaluated statistical methods for log-normally distributed variables, including the method of moments, maximum likelihood, and Finney's method. Parkin and Robinson (1993) evaluated soil properties using log-normal distribution. Brakensiek (1958) employed the least squares method for fitting the log-normal distribution to annual runoff. Moran (1957) fitted a log-normal distribution to fifty annual values of extreme monthly flow of the River Murray in Australia. Lewis (1979) applied log-normal distribution to maximum measured discharges of River Kafue in Africa.Weiss (1957) developed a nomogram for log-normal frequency analysis.Alexander et al. (1969) discussed statistical properties of lognormal distribution. Using mean square error of estimation as a criterion, Stedinger (1980) evaluated the efficiency of alternative methods of fitting the lognormal distribution. Charbeneau (1978) compared two- and three-parameter log-normal distributions for simulation of stream flow.