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Probability and Density Functions
2021This chapter deals with discussion of important probability density functions used in practice.
Chandrasekhar Putcha +2 more
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THE MARGINAL PROBABILITY DENSITY FUNCTIONS OF WISHART PROBABILITY DENSITY FUNCTION
Far East Journal of Theoretical Statistics, 2018Summary: Here we directly evaluate an \(\begin{pmatrix}{m+1}\\{2}\end{pmatrix}\)-dimensional integral \[ \int_{\mathbf{S}_{m}>0}|\mathbf{S}_m|^{\frac{n-m}{2}-1}\exp(-\mathrm{tr}(\mathbf{S}_{\mathbf{m}}))\mathrm{d}\mathbf{S}_m \] as an integral representation of Wishart multivariate gamma function \(\Gamma_m\left(\frac{n-1}{2}\right)\), by deriving the ...
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2019
Abstract This chapter builds on probability distributions. Its focus is on general concepts associated with probability density functions (pdf’s), which are distributions associated with continuous random variables. The continuous uniform and normal distributions are highlighted as examples of pdf’s.
Therese M. Donovan, Ruth M. Mickey
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Abstract This chapter builds on probability distributions. Its focus is on general concepts associated with probability density functions (pdf’s), which are distributions associated with continuous random variables. The continuous uniform and normal distributions are highlighted as examples of pdf’s.
Therese M. Donovan, Ruth M. Mickey
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Probability density functions of soft information
IEEE Communications Letters, 2002It is well known that soft decoding algorithms are based on the use of reliability measures for binary and nonbinary symbols. We consider an analytical estimation of the distributions of reliability measures after soft decoding of block and convolutional codes or intersymbol interference (ISI) channels.
REGGIANI, LUCA, TARTARA, GUIDO
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Estimation of a certain functional of a probability density function
Scandinavian Actuarial Journal, 1969Abstract In nonparametric inference, the importance of the functional Δ(F)=∫−∞∞ ƒ2(x)dx, where F is the population cdf with density f, could hardly be overemphasized. It is a fundamental quantity involved in the expressions for the asymptotic efficiency of rank tests for many problems like location shift, regression, dependence, analysis of variance ...
Bhattacharyya, G. K., Roussas, G. G.
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Navier-stokes probability density function
European Journal of Mechanics - B/Fluids, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Minotti, F. O., Ferro Fontán, C.
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ON THE DENSITIES OF PROBABILITY MEASURES IN FUNCTION SPACES
Russian Mathematical Surveys, 1966CONTENTSIntroduction § 1. Basic facts from the theory of stochastic processes § 2. Characteristic functionals of stochastic processes § 3. General theorems on the absolute continuity of probability measures in function spaces § 4. Absolute continuity of Gaussian measures in Hilbert space § 5.
Gikhman, I. I., Skorokhod, A. V.
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Estimation of probability density and distribution functions
IEEE Transactions on Information Theory, 1968First- and second-order stochastic gradient algorithms are developed for suitably approximating the unknown density and distribution functions of a random vector from a sequence of independent samples. The mean-square-error criterion and the integral-square-error criterion are used in the approximations.
R. L. Kashyap, Colin C. Blaydon
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On system failure probability density function
Reliability Engineering & System Safety, 2007Abstract The assessment of the system unreliability is usually accomplished through well-known tools such as block diagram, fault tree, Monte Carlo and others. These methods imply the knowledge of the failure probability density function of each component “k” (pdf p k ).
Campioni L., VESTRUCCI, PAOLO
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Cluster Width of probability Density functions
Intelligent Data Analysis, 2019This study establishes the new results for Cluster Width of probability Density functions (CWD). There are the upper and lower bounds of CWD and the relationships of CWD to other measures in statistical discriminant. The CWD for two and more two probability density functions is determined in the different cases.
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