\r\ngiven portion of territory is fundamental for the monitoring of

\r\nclimatic conditions and for Hydrogeological Management Plans

\r\n(HMP). This modelling is rendered particularly complex by the

\r\nchanges taking place in the frequency and intensity of precipitation,

\r\npresumably to be attributed to the global climate change. This paper

\r\napplies the Wakeby distribution (with 5 parameters) as a theoretical

\r\nreference model. The number and the quality of the parameters

\r\nindicate that this distribution may be the appropriate choice for

\r\nthe interpolations of the hydrological variables and, moreover, the

\r\nWakeby is particularly suitable for describing phenomena producing

\r\nheavy tails. The proposed estimation methods for determining the

\r\nvalue of the Wakeby parameters are the same as those used for

\r\ndensity functions with heavy tails. The commonly used procedure

\r\nis the classic method of moments weighed with probabilities

\r\n(probability weighted moments, PWM) although this has often shown

\r\ndifficulty of convergence, or rather, convergence to a configuration

\r\nof inappropriate parameters. In this paper, we analyze the problem of

\r\nthe likelihood estimation of a random variable expressed through its

\r\nquantile function. The method of maximum likelihood, in this case,

\r\nis more demanding than in the situations of more usual estimation.

\r\nThe reasons for this lie, in the sampling and asymptotic properties of

\r\nthe estimators of maximum likelihood which improve the estimates

\r\nobtained with indications of their variability and, therefore, their

\r\naccuracy and reliability. These features are highly appreciated in

\r\ncontexts where poor decisions, attributable to an inefficient or

\r\nincomplete information base, can cause serious damages.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 148, 2019"}