Topic
Probability density function
About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.
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26 Oct 2009
TL;DR: Electromagnetic fields in cavities: Deterministic and statistical theories is a book about magnetism and cavities that explains the behaviour of magnetospheres in terms of determinants and statistical theory.
Abstract: PREFACE. PART I. DETERMINISTIC THEORY. 1. Introduction. 1.1 Maxwell's Equations. 1.2 Empty Cavity Modes. 1.3 Wall Losses. 1.4 Cavity Excitation. 1.5 Perturbation Theories. Problems. 2. Rectangular Cavity. 2.1 Resonant Modes. 2.2 Wall Losses and Cavity Q. 2.3 Dyadic Green's Functions. Problems. 3. Circular Cylindrical Cavity. 3.1 Resonant Modes. 3.2 Wall Losses and Cavity Q. 3.3 Dyadic Green's Functions. Problems. 4. Spherical Cavity. 4.1 Resonant Modes. 4.2 Wall Losses and Cavity Q. 4.3 Dyadic Green's Functions. 4.4 Schumann Resonances in the Earth-Ionosphere Cavity. Problems. PART II. STATISTICAL THEORIES FOR ELECTRICALLY LARGE CAVITIES. 5. Motivation for Statistical Approaches. 5.1 Lack of Detailed Information. 5.2 Sensitivity of Fields to Cavity Geometry and Excitation. 5.3 Interpretation of Results. Problems. 6. Probability Fundamentals. 6.1 Introduction. 6.2 Probability Density Function. 6.3 Common Probability Density Functions. 6.4 Cumulative Distribution Function. 6.5 Methods for Determining Probability Density Functions. Problems. 7. Reverberation Chambers. 7.1 Plane-Wave Integral Representation of Fields. 7.2 Ideal Statistical Properties of Electric and Magnetic Fields. 7.3 Probability Density Functions for the Fields. 7.4 Spatial Correlation Functions of Fields and Energy Density. 7.5 Antenna or Test-Object Response. 7.6 Loss Mechanisms and Chamber Q. 7.7 Reciprocity and Radiated Emissions. 7.8 Boundary Fields. 7.9 Enhanced Backscatter at the Transmitting Antenna. Problems. 8. Aperture Excitation of Electrically Large, Lossy Cavities. 8.1 Aperture Excitation. 8.2 Power Balance. 8.3 Experimental Results for SE. Problems. 9. Extensions to the Uniform-Field Model. 9.1 Frequency Stirring. 9.2 Unstirred Energy. 9.3 Alternative Probability Density Function. Problems. 10. Further Applications of Reverberation Chambers. 10.1 Nested Chambers for Shielding Effectiveness Measurements. 10.2 Evaluation of Shielded Enclosures. 10.3 Measurement of Antenna Efficiency. 10.4 Measurement of Absorption Cross Section. Problems. 11. Indoor Wireless Propagation. 11.1 General Considerations. 11.2 Path Loss Models. 11.3 Temporal Characteristics. 11.4 Angle of Arrival. 11.5 Reverberation Chamber Simulation. Problems. APPENDIX A. VECTOR ANALYSIS. APPENDIX B. ASSOCIATED LEGENDRE FUNCTIONS. APPENDIX C. SPHERICAL BESSEL FUNCTIONS. APPENDIX D. THE ROLE OF CHAOS IN CAVITY FIELDS. APPENDIX E. SHORT ELECTRIC DIPOLE RESPONSE. APPENDIX F. SMALL LOOP ANTENNA RESPONSE. APPENDIX G. RAY THEORY FOR CHAMBER ANALYSIS. APPENDIX H. ABSORPTION BY A HOMOGENEOUS SPHERE. APPENDIX I. TRANSMISSION CROSS SECTION OF A SMALL CIRCULAR APERTURE. APPENDIX J. SCALING. REFERENCES. INDEX.
353 citations
TL;DR: In this article, a sample of eight quasars observed at high resolution and signal-to-noise ratio is used to determine the transmitted flux probability distribution function (TFPDF), and the power spectrum and correlation function of the transmitted transmitted flux in the Lyα forest, in three redshift bins centered at z = 2.41, 3.00, and 3.89.
Abstract: A sample of eight quasars observed at high resolution and signal-to-noise ratio is used to determine the transmitted flux probability distribution function (TFPDF), and the power spectrum and correlation function of the transmitted flux in the Lyα forest, in three redshift bins centered at z = 2.41, 3.00, and 3.89. All the results are presented in tabular form, with full error covariance matrices, to allow for comparisons with any numerical simulations and with other data sets. The observations are compared with a numerical simulation of the Lyα forest of a ΛCDM model with Ω = 0.4, known to agree with other large-scale structure observational constraints. There is excellent agreement for the TFPDF if the mean transmitted flux is adjusted to match the observations. A small difference between the observed and predicted TFPDF is found at high fluxes and low redshift, which may be due to the uncertain effects of fitting the spectral continuum. Using the numerical simulation, we show how the flux power spectrum can be used to recover the initial power spectrum of density fluctuations. From our sample of eight quasars, we measure the amplitude of the mass power spectrum to correspond to a linear variance per unit ln k of Δ(k) = 0.72 ± 0.09 at k = 0.04(km s-1)-1 and z = 3, and the slope of the power spectrum near the same k to be np = -2.55 ± 0.10 (statistical error bars). The results are statistically consistent with those of Croft et al., although our value for the rms fluctuation is lower by a factor of 0.75. For the ΛCDM model we use, the implied primordial slope is n = 0.93 ± 0.10, and the normalization is σ8 = 0.68 + 1.16(0.95 - n) ± 0.04.
351 citations
TL;DR: The key idea is to align the complexity level and order of analysis with the reliability and detail level of statistical information on the input parameters to avoid the necessity to assign parametric probability distributions that are not sufficiently supported by limited available data.
350 citations
TL;DR: An approach combining elements of both histograms and probability density distributions is proposed and all methods are applied in an Excel workbook and the procedures for using this are explained.
345 citations
TL;DR: In this article, the authors considered the turbulent homogeneous mixing of two reactants undergoing a one step, second order, irreversible, exothermic chemical reaction with a rate constant of the Arrhenius type.
344 citations