Three-Parameter Lognormal Distribution

Abstract

The three-parameter lognormal (TPLN)distribution is frequently used in hydrologic analysis of extreme floods, seasonal flow volumes, duration curves for daily streamflow, rainfall intensity-duration, soil water retention, etc. It is also popular in synthetic streamflow generation. Properties of this distribution are discussed by Aitchison and Brown (1957), and Johnson and Kotz (1970). Its applications are discussed by Slade (1936), Chow (1954), Matalas (1967), Sangal and Biswas (1970), Fiering and Jackson (1971), Snyder and Wallace (1974), Burges et al. (1975), Burges and hoshi (1978), Charbeneau (1978), Stedinger (1980), Singh and Singh (1987), Kosugi (1994), among others. Burges et al. (1975) discussed properties of the three-parameter lognormal distribution and compared two methods of estimation of the third parameter ``a''. Kosugi (1994) applied the three-parameter lognormal distribution to the pore radius distribution function and to the water capacity function which was taken to be the pore capillary distribution function. He found that three parameters were closely related to the statistics of the pore capillary pressure distribution function, including the bubbling pressure, the mode of capillary pressure, and the standard deviation of transformed capillary distribution function. Burges and Hoshi (1978) proposed approximating the normal populations with 3-parameter lognormal distributions to facilitate multivariate hydrologic disaggregation or generation schemes in cases where mixed normal and lognormal populations existed.