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Estimation of a probability density function and its derivatives

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Abstract

We investigate statistical estimates of a probability density distribution function and its derivatives. As the starting point of the investigation we take a priori assumptions about the degree of smoothness of the probability density to be estimated. By using these assumptions we can construct estimates of the probability density function itself and its derivatives which are distinguished by the high rate of decrease of the error in the estimate as the sample size increases.

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Authors and Affiliations

  1. Institute of Physics of the Atmosphere, Academy of Sciences of the USSR, USSR

    V. G. Alekseev

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  1. V. G. Alekseev
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, 621–626, November, 1972.

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Alekseev, V.G. Estimation of a probability density function and its derivatives. Mathematical Notes of the Academy of Sciences of the USSR 12, 808–811 (1972). https://doi.org/10.1007/BF01099071

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  • DOI: https://doi.org/10.1007/BF01099071

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