scholarly journals Divergence & Probability Density : A Hypothesis

2020 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Probability Density ◽  
Multiplication Rule ◽  
Multiplicative Rule ◽  
Algebraic Properties

The earlier work by Datta et al ( 1 ) the note has been made with the algebraic properties of Probability ie P (A) +P(B )= P ( A*B ) . This is termed as multiplicative rule of Probability. By multiplication rule any number say a can be first diverged through a series of a ( pow ) x , Where x is an integer like 0 to n . REF :PROBABILITY & WAVEFUNCTION : A NOTE November 2019 DOI: 10.31219/osf.io/awk96

PROBABILITY: A NOTE

2020 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probabilistic Approach ◽  
Wave Functions ◽  
P Wave ◽  
Multiplicative Rule

Wave Function , Probability Density Function , Multiplicative Probability , Partition function .In this note we correlate a quantum normalized probabilistic approach with Algebric approach of Probability . The Probability Density [ Shi ]^2 may be equated as additive wave functions ie [Shi A] +[ Shi B ] . In real probability algebra we also know that P(A) +P(B )= P ( A*B ) . This is termed as multiplicative rule of Probability . Greater is P ( A*B ) = [ Shi ] ^2 greater will be the Probability Density F( x ) .

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

A Delta-Sigma Modulator Using a Non-uniform Quantizer Adjusted for the Probability Density of Input Signals

2012 ◽  
Vol E95.B (7) ◽  
pp. 2257-2265
Author(s):  
Toru KITAYABU ◽  
Mao HAGIWARA ◽  
Hiroyasu ISHIKAWA ◽  
Hiroshi SHIRAI
Keyword(s):  
Probability Density ◽  
Delta Sigma Modulator ◽  
Delta Sigma ◽  
Input Signals
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