The use of kernel estimators to determine the distribution of groundwater level

• Autorzy: Michalski A.
• Języki publikacji: EN

Abstrakty

EN

In this paper the problem of non-parametric estimation of the probability density function for hydrological data is considered. For a given random sample X1, X2, ..., Xn we define an estimator fˆ n of the density function ƒ based on a function K of a real variable – the so-called kernel of a distribution – and a properly chosen number sequence {hn} from the interval (0, ∞). This estimator of density function of a random variable X under more general assumptions is known in the statistical literature as the Parzen-Rosenblatt estimator or the kernel estimator. The method of kernel estimation presented in the paper has been applied to determine the probability distribution of the groundwater level based on long-term measurements made in the melioration research carried out at the foothill object Długopole.

Słowa kluczowe

EN

probability density function; kernel density estimator; groundwater level

• Wydawca: Instytut Meteorologii i Gospodarki Wodnej - Państwowy Instytut Badawczy
• Czasopismo: Meteorology Hydrology and Water Management. Research and Operational Applications
• Rocznik: 2016
• Tom: Vol. 4, Iss. 1
• Strony: 41--46
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Michalski A.

• Wrocław University of Environmental and Life Sciences, Department of Mathematics, Grunwaldzka 53, 50-357 Wrocław, Poland

Bibliografia

• Akaike H., 1954, An approximation to the density function, Annals of the Institute of Statistical Mathematics, 6 (2), 127-132, DOI: 10.1007/BF02900741
• Berlinet A., Devroye L., 1994, A comparison of kernel density estimates, Publications de l’Institut de Statistique de l’Université de Paris, XXXVIII – Fascicule, 3, 3-59
• Devroye L., 1989, The double kernel method in density estimation, Annales de l’Institut Henri Poincaré, 25, 533-580
• Devroye L., 1992, A note on the usefulness of superkernels in density estimation, Annals of Statistics, 20 (4), 2037-2056
• Devroye L., Wagner, T.J., 1976, Nonparametric discrimination and density estimation, Technical Report 183, Electronic Research Center the University of Texas at Austin, TX, USA
• Gajek L., Kałuszka M., 1994, Statistical Inference, Wydawnictwo Naukowo-Techniczne, Warsaw, 304 pp., (in Polish)
• Gąsiorek E., Michalski A., Pływaczyk A., 1990, Analysis of land improvement objects data, Zeszyty Naukowe Akademii Rolniczej we Wrocławiu, 65-76, (in Polish)
• Kuchar L., 2004, Using WGENK to generate synthetic daily weather data for modeling of agricultural processes, Mathematics and Computers in Simulation, 65 (1-2), 69-75, DOI: 10.1016/j.matcom.2003.09.009
• Kuchar L., Iwański S., Jelonek L., Szalińska W., 2014, Application of spatial weather generator for the assessment of climate change impacts on a river runoff, Geografie, 119 (1), 1-25
• Nadaraya E.A., 1965, On nonparametric estimation of density functions and regression curves, Theory of Probability and Its Applications, 10 (1), 186-190, DOI: 10.1137/1110024
• Parzen E., 1962, On the estimation of a probability density function and the mode, Annals of Mathematical Statistics, 33 (3), 1065-1076, DOI: 10.1214/aoms/1177704472
• Rosenblatt M., 1956, Remarks on some nonparametric estimates of a density function, Annals of Mathematical Statistics, 27 (3), 832-837, DOI:10.1214/aoms/1177728190
• Schuster E.F., 1969, Estimation of a probability density function and its derivatives, The Annals of Mathematical Statistics, 40 (4), 1187-1195
• Scott D.W., 1992, Multivariate density estimation. Theory, Practice and Visualization, John Wiley & Sons Inc., New York, USA , 317 pp., DOI: 10.1002/9780470316849
• Silverman B.W., 1986, Density estimation for statistics and data analysis, CRC Press, London, UK, 176 pp.
• Van Ryzin J., 1969, On strong consistency of density estimates, Annals of Mathematical Statistics, 40 (5), 1765-1772
• Watson G.S., Leadbetter M.R., 1963, On the estimation of the probability density, Annals of Mathematical Statistics, 34 (2), 480-491
• Wegman E.J., 1972, Nonparametric probability density estimation, I: A summary of a variable methods, Technometrics, 14 (3), 533-546, DOI: 10.1080/00401706.1972.1048894