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Books on the topic 'Estimation of probability density function'

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Published: 30 May 2022
Last updated: 31 May 2022

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1

Baram, Yoram. Estimation and classification by sigmoids based on mutual information. [Washington, D.C: National Aeronautics and Space Administration, 1994.

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2

Devroye, Luc. Nonparametric density estimation: The L1 view. New York: Wiley, 1985.

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3

László, Györfi, ed. Nonparametric density estimation: The L₁ view. New York: Wiley, 1985.

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4

Churnside, James H. Probability density function of optical scintillations (scintillation distribution). Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1989.

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5

R, Thompson James. Nonparametric function estimation, modeling, and simulation. Philadelphia: Society for Industrial and Applied Mathematics, 1990.

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6

Yamazaki, Hidekatsu. Determination of wave height spectrum by means of a joint probability density function. College Station, Tex: Sea Grant College Program, Texas A & M University, 1985.

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7

Fornari, Fabio. Recovering the probability density function of asset prices using GARCH as diffusion approximations. [Roma]: Banca d'Italia, 2001.

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8

Fornari, Fabio. The probability density function of interest rates implied in the price of options. Rome: Banca d'Italia, 1998.

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9

Ma, Xiaofang. Computation of the probability density function and the cumulative distribution function of the generalized gamma variance model. Ottawa: National Library of Canada, 2002.

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10

Simon, M. Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device. Pasadena, Calif: National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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11

Ryu, Hang Keun. Orthonormal basis and maximum entropy estimation of probability density and regression functions. 1990.

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12

Hall, Peter. Principal component analysis for functional data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.8.

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This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.
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13

Devroye, Luc. Combinatorial Methods in Density Estimation. Springer, 2012.

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14

Lugosi, Gabor, and Luc Devroye. Combinatorial Methods in Density Estimation. Springer, 2001.

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15

J, Lataitis R., and Wave Propagation Laboratory, eds. Probability density function of optical scintillations (scintillation distribution). Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Wave Propagation Laboratory, 1989.

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16

Tapia, Richard A., and James R. Thompson. Nonparametric Function Estimation, Modeling, and Simulation. Society for Industrial Mathematics, 1987.

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17

Topcu, Mehmet. Measured probability density function of a phased-locked loop output. 1987.

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18

Tapia, Richard A., and James R. Thompson. Nonparametric Probability Density Estimation (Johns Hopkins Studies in the Mathematical Sciences). Johns Hopkins University Press, 2002.

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19

Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley Series in Probability and Statistics). 2nd ed. Wiley-Interscience, 2006.

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20

Rossi, Richard J. Nonparametric density estimation by generalized expansion estimators-a cross-validation approach. 1988.

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21

EUPDF, an Eulerian-based Monte Carlo probability density function (PDF) solver: User's manual. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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22

Center, Lewis Research, ed. EUPDF, an Eulerian-based Monte Carlo probability density function (PDF) solver: User's manual. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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23

EUPDF, an Eulerian-based Monte Carlo probability density function (PDF) solver: User's manual. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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24

VanMarcke, E. H. Quantum Origins of Cosmic Structure: Probability Density Function of Quantity-mass-ratio Logarithm. Swets & Zeitlinger Publishers, 1997.

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25

Center, Lewis Research, ed. EUPDF, an Eulerian-based Monte Carlo probability density function (PDF) solver: User's manual. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1998.

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26

Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device. Pasadena, Calif: National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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27

Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device. Pasadena, Calif: National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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28

J, Mileant, and Jet Propulsion Laboratory (U.S.), eds. Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device. Pasadena, Calif: National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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29

Standard Guideline for Fitting Saturated Hydraulic Conductivity Using Probability Density Function and Standard Guideline for Calculating the Effective Saturated Hydraulic Conductivity. Reston, VA: American Society of Civil Engineers, 2008. http://dx.doi.org/10.1061/9780784409930.

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30

Lattman, Eaton E., Thomas D. Grant, and Edward H. Snell. Pushing the Envelope. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199670871.003.0014.

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Direct electron density determination from SAXS data opens up new opportunities. The ability to model density at high resolution and the implicit direct estimation of solvent terms such as the hydration shell may enable high-resolution wide angle scattering data to be used to calculate density when combined with additional structural information. Other diffraction methods that do not measure three-dimensional intensities, such as fiber diffraction, may also be able to take advantage of iterative structure factor retrieval. While the ability to reconstruct electron density ab initio is a major breakthrough in the field of solution scattering, the potential of the technique has yet to be fully uncovered. Additional structural information from techniques such as crystallography, NMR, and electron microscopy and density modification procedures can now be integrated to perform advanced modeling of the electron density function at high resolution, pushing the boundaries of solution scattering further than ever before.
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31

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.
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32

Boudreau, Joseph F., and Eric S. Swanson. Data modeling. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0016.

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A variety of techniques for extracting information from data are presented, from pedestrian approaches such as the centuries old linear least-squares fit, to elegant binned and unbinned likelihood fits. A treatment of statistical combination of data leads to an introduction to the powerful Kalman filter approach, used to determine optimal estimates of deterministic-stochastic systems. In experimental physics the Kalman filter is used estimate trajectories from data, but it also finds applications in industrial process control, and in the aeronautics and robots industries. These techniques typically rely on either analytic or numerical optimization of an objective function. Orthogonal series density estimation, a Fourier technique, is also discussed.
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33

Rhomari, Noureddine. On Bernstein Type and Maximal Inequalities for Dependent Banach-Valued Random Vectors and Applications. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.14.

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This article discusses some results on Bernstein type and maximal inequalities for partial sums of dependent random vectors taking their values in separable Hilbert or Banach spaces of finite or infinite dimension. Two types of measure of dependence are considered: strong mixing coefficients (α-mixing) and absolutely regular mixing coefficients (β-mixing). These inequalities, which are similar to those in the dependent real case, are used to derive the strong law of large numbers (SLLN) and the bounded law of the iterated logarithm (LIL) for absolutely regular Hilbert- or Banach-valued processes under minimal mixing conditions. The article first introduces the relevant notation and definitions before presenting the maximal inequalities in the strong mixing case, followed by the absolutely regular mixing case. It concludes with some applications to the SLLN, the bounded LIL for Hilbertian or Banachian absolutely regular processes, the recursive estimation of probability density, and the covariance operator estimations.
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34

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.
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35

Mann, Peter. The Harmonic Oscillator. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0004.

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This chapter discusses the harmonic oscillator, which is a model ubiquitous to all branches of physics. The harmonic oscillator is a system with well-known solutions and has been fully investigated since it was first developed by Robert Hooke in the seventeenth century. These factors ensure that the harmonic oscillator is as relevant to a swinging pendulum as it is to a quantum field. Due to the importance of this model, the chapter investigates its dynamical properties, including the superposition principle in solutions, and construct a probability density function in a single dimension. The chapter also discusses Hooke’s law, modes and the Morse potential. In addition, in an exercise, the chapter introduces series solutions to ordinary differential equations.
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36

Brezin, Edouard, and Sinobu Hikami. Beta ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.20.

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This article deals with beta ensembles. Classical random matrix ensembles contain a parameter β, taking on the values 1, 2, and 4. This parameter, which relates to the underlying symmetry, appears as a repulsion sβ between neighbouring eigenvalues for small s. β may be regarded as a continuous positive parameter on the basis of different viewpoints of the eigenvalue probability density function for the classical random matrix ensembles - as the Boltzmann factor for a log-gas or the squared ground state wave function of a quantum many-body system. The article first considers log-gas systems before discussing the Fokker-Planck equation and the Calogero-Sutherland system. It then describes the random matrix realization of the β-generalization of the circular ensemble and concludes with an analysis of stochastic differential equations resulting from the case of the bulk scaling limit of the β-generalization of the Gaussian ensemble.
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37

Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.
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38

Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).
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