Studying the HALPHEN DISTRIBUTION FAMILY was suggested by Professor Jacques Bernier, a visiting scientist at the Chair in Statistical Hydrology. In this book the authors put together theoretical works from the advances that have been made in the last twenty years, such as: - Statistical analysis, which has become an important tool in water resources management and planning, and; - Hydrological frequency analysis, which is a particularly useful method to estimate the probability of occurrence of a given event by fitting a statistical distribution to a sample of independent and identically distributed data. The desirable statistical properties of these three distributions (complete system and optimal properties of the estimators) motivated the researchers to thoroughly study this system. Chapters 2 to 4 comprehensively discuss each of the three Halphen distributions: - Mathematical and statistical properties; - Asymptotic behavior and model selection; - Parameter estimation methods. Chapter 5 is concerned with the simulation and generation of samples from Halphen distributions. Matlab codes for Halphen fitting and generating are included in Chapter 6. This book will be a useful resource to scientists, engineers, and specialists involved statistical in hydrology and water resources management and planning.