scholarly journals Probability Densities for Fluorescent Photons Emitted by a Two-State Atom Driven by a Laser

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Robertsen A. Riehle ◽  
Henk F. Arnoldus
Keyword(s):  
Laser Beam ◽  
Probability Density ◽  
Initial Time ◽  
Independent Events ◽  
Probability Densities

Fluorescent photons emitted by a two-state atom in a laser beam are correlated. We have obtained the probability density for the emission of the th photon after a random initial time . It is shown that the correlations between the photons lead to a deviation from the poissonian value for this function (the probability density for independent events), although the deviation is not as significant as one may expect.

The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

1973 ◽  
Vol 59 (3) ◽  
pp. 537-559 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh
Keyword(s):  
Reynolds Number ◽  
Probability Density ◽  
Streamwise Velocity ◽  
Statistical Characteristics ◽  
Large Reynolds Number ◽  
Higher Moments ◽  
Scale Similarity ◽  
Probability Densities ◽  
Scale Ratio ◽  
Velocity Derivative

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂tmeasured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficientqr,lof the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values ofqr,land measurements of higher moments indicate that the assumption that the probability densities for adjoint values ofqr,lare statistically independent is also not satisfied. The moments ofqr,ldo not have the simple power-law character that is a consequence of scale similarity.As the scale ratiol/rchanges, the probability density ofqr,levolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

scholarly journals Computation of Power Loss in Likelihood Ratio Tests for Probability Densities Extended by Lehmann Alternatives

2018 ◽  
Author(s):  
Lucas Gallindo
Keyword(s):  
Probability Density ◽  
Likelihood Ratio ◽  
Power Loss ◽  
Likelihood Ratio Tests ◽  
Probability Densities ◽  
Lehmann Alternative

We compute the loss of power in likelihood ratio tests when we test the original parameter of a probability density extended by the first Lehmann alternative.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Quantum Process ◽  
Hidden Variable ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

scholarly journals PROBABILITIES OF BREAKING WAVE CHARACTERISTICS

1970 ◽  
Vol 1 (12) ◽  
pp. 25 ◽  
Author(s):  
J. Ian Collins
Keyword(s):  
Shallow Water ◽  
Probability Density ◽  
Deep Water ◽  
Surf Zone ◽  
Probability Distributions ◽  
Rayleigh Distribution ◽  
Breaking Wave ◽  
Wave Characteristics ◽  
Probability Densities ◽  
Wave Heights

Utilizing the hydrodynamic relationships for shoaling and refraction of waves approaching a shoreline over parallel bottom contours a procedure is developed to transform an arbitrary probability density of wave characteristics in deep water into the corresponding breaking characteristics in shallow Water A number of probability distributions for breaking wave characteristics are derived m terms of assumed deep water probability densities of wave heights wave lengths and angles of approach Some probability densities for wave heights at specific locations in the surf zone are computed for a Rayleigh distribution in deep water The probability computations are used to derive the expectation of energy flux and its distribution.

scholarly journals Diameter structure of the stands of poplar clones

2010 ◽  
Vol 56 (No. 4) ◽  
pp. 165-170 ◽  
Author(s):  
R. Petráš ◽  
J. Mecko ◽  
V. Nociar
Keyword(s):  
Probability Density ◽  
Small Variation ◽  
Skewed Distribution ◽  
Likelihood Method ◽  
Weibull Function ◽  
Frequency Distributions ◽  
Poplar Clones ◽  
Mean Diameter ◽  
Probability Densities ◽  
Diameter Structure

The construction of a continuous mathematical model of frequency distributions of the diameters of trees of poplar clones Robusta and I-214 in dependence on tree diameter and mean diameter of stand is presented. Empirical material consists of diameter measurements on research plots from poplar regions in Slovakia. There were 90 plots for I-214 clone and 142 plots for Robusta clone. There were about 10–250 trees with mean diameter 2–70 cm on the research plots. The model was derived according to the three-parameter Weibull function. Its parameters were estimated by maximum likelihood method of the logarithm of the probability density function. Smoothed sample probability densities were processed in continuous mathematical models where the probability density of trees in stands is a function of their diameters and mean diameter of the stand. The method of regression smoothing of the parameters of Weibull function from sample sets in dependence on their mean diameter was used. In the whole range of mean diameters both clones have slightly left-skewed distribution with a relatively small variation range.

scholarly journals Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues

2018 ◽  
Vol 50 (2) ◽  
pp. 373-395 ◽  
Author(s):  
Dmitri Finkelshtein ◽  
Pasha Tkachov
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Probability Density ◽  
Real Line ◽  
The Real ◽  
Probability Densities ◽  
Tail Asymptotic

Abstract We study the tail asymptotic of subexponential probability densities on the real line. Namely, we show that the n-fold convolution of a subexponential probability density on the real line is asymptotically equivalent to this density multiplied by n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular subexponential functions and use it to find an analogue of Kesten's bound for functions on ℝd. The results are applied to the study of the fundamental solution to a nonlocal heat equation.

scholarly journals A Search for A Stochastic Archetype of Quantum Probability

2021 ◽  
Vol 4 (4) ◽  
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Quantum Process ◽  
Hidden Variable ◽  
Probability Densities

Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability

Estimation of the integral of the square of derivatives of symmetric probability densities of one-dimensional random variables

Metrologiya ◽  
2020 ◽  
pp. 15-27
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Standard Deviation ◽  
Probability Density ◽  
Random Variables ◽  
Random Variable ◽  
Density Estimates ◽  
One Dimensional ◽  
Probability Densities ◽  
The One ◽  
Derivatives Of ◽  
Selection Of

When substantiating the method of fast selection of the bandwidth of kernel probability density estimates, a constant was found that is a functional of the second density derivative. In this paper, the obtained result is generalized to derivatives of symmetric probability densities of different orders. The functional dependences of the constants under study on the coeffi cient of antikurtosis of a random variable are established. The regularities peculiar to them are investigated. Based on the results obtained, a method for estimating functionals from derived probability densities has been developed, which involves the following actions. In the original sample estimated standard deviation of the one-dimensional random variables and the coeffi cient of antikurtosis. Using the reconstructed functional dependences on the antikurtosis coeffi cient, the constants are estimated, which are functionals of the derivatives of the probability density. With known estimates of the standard deviation of the investigated random variable and the considered constant, the values of the functional from the derivative of the probability density of the selected order are calculated. The obtained results are confi rmed by the analysis of the data of computational experiments. It is established that with increasing order of the derivative, the values of the estimates of the studied functionals increase. This fact is explained by the complication of the integrand function in the considered functionals. The proposed method provides objective results for the fi rst three derivatives of the probability density of a random variable. The obtained conclusions are confi rmed by the results of the confi dence estimation of the investigated functionals.

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