Five-parameter log-normal distribution and its modification

Budíková, Marie and Holub, Jan and Budík, Ladislav and Přibylová, Lenka and Horová, Ivana (2025) Five-parameter log-normal distribution and its modification. IDŐJÁRÁS / QUARTERLY JOURNAL OF THE HUNGARIAN METEOROLOGICAL SERVICE, 129 (2). pp. 133-160. ISSN 0324-6329

Preview

Text 9111254f54adca3724293ccff6f19e0d-129-2-2-budikova.pdf - Published Version Download (5MB) | Preview

Abstract

The introduction of the LN5 and mLN5 distributions extends the commonly used three-parameter log-normal distribution (LN3) by enhancing tail modeling, which is critical for accurate representation of extreme values in hydrology and climatology. This paper details two methods for parameter estimation: the established local maximum likelihood method and the newly developed triangular method, an adaptation of the relative least squares approach. The effectiveness of these distributions is demonstrated through their application to datasets from the Czech Hydrometeorological Institute, encompassing average daily flow, precipitation, atmospheric pressure, and air temperature. Results show significant improvements in modeling extreme events with LN5 and mLN5 over LN3, as well as over other compared distributions such as generalized Gamma and generalized Weibull, particularly in tail behavior, underscoring their potential for advancing environmental studies. Appendices include comprehensive derivations of the functional characteristics of LN5 and mLN5 and introduce an alternative parametrization for LN5.

Actions (login required)

Edit Item