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1

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

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2

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

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3

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

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4

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

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5

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

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6

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

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7

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

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8

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

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9

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

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10

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. National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, 1986.

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11

United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Probability density functions in turbulent channel flow. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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12

United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Probability density functions in turbulent channel flow. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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13

Ronald, Johnson L., Smith P. L, and United States. National Aeronautics and Space Administration., eds. Probability density functions of observed rainfall in Montana. National Aeronautics and Space Administration, 1995.

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14

Ronald, Johnson L., Smith P. L, and United States. National Aeronautics and Space Administration., eds. Probability density functions of observed rainfall in Montana. National Aeronautics and Space Administration, 1995.

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15

Canada, Atomic Energy of. Guidelines for defining probability density functions for SYVAC3-CC3 parameters. Atomic Energy of Canada Limited, 1989.

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16

Moek, G. Verification of obstacle accountability areas using a simple mathematical model. Part I: Description of general model and application for a specific case. National Aerospace Laboratory, 1985.

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17

Bahra, Bhupinder. Implied risk-neutral probability density functions from option prices: Theory and application. Bank of England, 1997.

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18

Bahra, Bhupinder. Implied risk-neutral probability density functions from option prices: Theory and application. Bank of England, 1997.

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19

Morrison, Desmond Kenneth. Display of probability density functions using the PC and MC68HC711 micro-controller. The Author], 1994.

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20

Brenner, Marty. Nonstationary dynamics data analysis with wavelet-SVD filtering. National Aeronautics and Space Administration, Dryden Flight Research Center, 2001.

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21

Moek, G. Approximate confidence regions for the parameters of three software reliability models. National Aerospace Laboratory, 1987.

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22

Robert, Rubinstein, and Institute for Computer Applications in Science and Engineering., eds. Mapping closure approximation to conditional dissipation rate for turbulent scalar mixing. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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23

N, Singhal Surendra, Chamis C. C, and United States. National Aeronautics and Space Administration., eds. Reliability, risk and cost trade-offs for composite designs. National Aeronautics and Space Administration, 1996.

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24

John F. Kennedy Space Center. and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. Statistical short-range guidance for peak wind speed forecasts on Kennedy Space Center/Cape Canaveral Air Force Station: Phase 1 results. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 2002.

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25

John F. Kennedy Space Center. and United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., eds. Statistical short-range guidance for peak wind speed forecasts on Kennedy Space Center/Cape Canaveral Air Force Station: Phase 1 results. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 2002.

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26

Baram, Yoram. Estimation and classification by sigmoids based on mutual information. National Aeronautics and Space Administration, 1994.

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27

United States. National Aeronautics and Space Administration., ed. PDF methods for combustion in high-speed turbulent flows: Second annual technical report. National Aeronautics and Space Administration, 1995.

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28

Pope, Stephen B. PDF methods for combustion in high-speed turbulent flows: Second annual technical report. National Aeronautics and Space Administration, 1995.

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29

J, Hu, Hopkins D. A, and Lewis Research Center, eds. An overview of engineering concepts and current design algorithms for probabilistic structural analysis. NASA Lewis Research Center, 1995.

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30

United States. National Aeronautics and Space Administration., ed. A remote-sensing based technique to account for sub-grid scale variability of land surface properties. National Aeronautics and Space Administration, 1995.

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31

L, Crosson William, and United States. National Aeronautics and Space Administration., eds. Regional-scale hydrology with a new land surface processes model. National Aeronautics and Space Administration, 1995.

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32

L, Crosson William, and United States. National Aeronautics and Space Administration., eds. Regional-scale hydrology with a new land surface processes model. National Aeronautics and Space Administration, 1995.

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33

L, Crosson William, and United States. National Aeronautics and Space Administration., eds. Regional-scale hydrology with a new land surface processes model. National Aeronautics and Space Administration, 1995.

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34

American Society of Civil Engineers., ed. Standard guideline for fitting saturated hydraulic conductivity using probability density functions ASCE/EWRI 50-08: Standard guideline for calculating the effective saturated hydraulic conductivity ASCE/EWRI 51-08. American Society of Civil Engineers, 2008.

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35

Pierson, Willard J. Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989.

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36

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

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37

National Aeronautics and Space Administration (NASA) Staff. Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows. Independently Published, 2018.

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38

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

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39

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

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40

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

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41

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

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42

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

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43

American Society of Civil Engineers (ASCE). Standard Guideline for Fitting Saturated Hydraulic Conductivity Using Probability Density Function; Standard Guideline for Calculating the Effective Saturated Hydraulic Conductivity. American Society of Civil Engineers, 2008.

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44

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
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45

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

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46

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 expl
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47

Johler, J. R. Evaluation of the First and Second Moment Integrals of a Certain Probability Density Function by an Application of the Theory of Gaussian Quadrature; NBS Report 5595. Creative Media Partners, LLC, 2021.

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48

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 prese
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49

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 dis
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50

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 equ
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