In hydrologic frequency analysis, a variety of probability distribution functions, such as the gamma, log-normal, extreme-value, and log-gamma, are often examined whether they are appropriate to the flood data or not by using some hypothesis testing methods, because the properties of the flood data are not well understood even now. In order to find a property of the flood data, we can use another method: using the more general probability distribution function which includes many types of probability distributions used for hydrological statistics. The 4-parameter extended generalized gamma distribution function is one of such distribution functions. Two types of the extended distributions are proposed. The parameter estimation method is also introduced.