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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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Journal ArticleDOI
TL;DR: The principle of minimum cross-entropy (minimum directed divergence, minimum discrimination information) is a general method of inference about an unknown probability density when there exists a prior estimate of the density and new information in the form of constraints on expected values.
Abstract: The principle of minimum cross-entropy (minimum directed divergence, minimum discrimination information) is a general method of inference about an unknown probability density when there exists a prior estimate of the density and new information in the form of constraints on expected values. Various fundamental properties of cross-entropy minimization are proven and collected in one place. Cross-entropy's well-known properties as an information measure are extended and strengthened when one of the densities involved is the result of cross-entropy minimization. The interplay between properties of cross-entropy minimization as an inference procedure and properties of cross-entropy as an information measure is pointed out. Examples are included and general analytic and computational methods of finding minimum cross-entropy probability densities are discussed.

384 citations

Journal ArticleDOI
TL;DR: In this article, a probability theory involving multitime joint probability functions for a sequence of photoionizations is formulated, and approximate expressions for this probability function are derived for the photoionization detector and the electromagnetic field-plus-source.
Abstract: A theory of electromagnetic field measurement by means of photoionization is developed and applied to photoelectron counting. A probability theory involving multitime joint probability functions for a sequence of photoionizations is formulated. A general quantum-theory definition is proposed for the nonexclusive probability function which occurs in the probability theory. Approximations are then introduced to derive expressions for this probability function which involve correlation functions of the photoionization detector and the electromagnetic field-plus-source. The general theory is used to derive quantities of interest in photo-ionization counting experiments. Expressions are derived for (1) the probability ${P}_{n}(t, t+T)$ that $n$ photo-ionizations are observed in the time interval $t$ to $t+T$, and (2) quantities related to ${P}_{n}(t, t+T)$, such as its generating function and various moments. ${P}_{n}(t, t+T)$ is found to be a compound Poisson distribution determined by the density operator of the field when the latter is expressed in Glauber's $P$ representation. Using this result, the character of ${P}_{n}(t, t+T)$ is examined for several specific density operators. These correspond to a coherent state, various fields with the mode phases distributed independently of the mode amplitudes, and a "spread-out" coherent state.

382 citations

Journal ArticleDOI
TL;DR: In this paper, the probability density functions for one and three-dimensional fields in a mode-stirred chamber were derived and verified with chi-square goodness-of-fit tests on experimental data.
Abstract: The probability density functions for one- and three-dimensional fields in a mode-stirred chamber are derived and verified with chi-square goodness-of-fit tests on experimental data. Each of the three components of the field in the chamber is Rayleigh distributed, which is the same as chi distributed with six degrees of freedom. Each component of the power density is then exponentially distributed. Experimental data confirm these distributions, though unexpected high values, or outliers, were consistently found. Maximum-likelihood estimators of the functions' parameters are derived, and their accuracy is determined as a function of the amount of data. These results are applied to estimating chamber Q. The amount of data required for a given accuracy is determined. >

381 citations

Journal ArticleDOI
TL;DR: In this paper, the weighted average of the probability distribution function is recommended as the best central-point estimate, but more consideration should be given to using the full probability distribution rather than a point estimate in developing age-depth models.
Abstract: Intercept-based methods of generating a point estimate of a calibrated radiocarbon date are very popular, but exhibit undesirable behaviour. They are highly sensitive to the mean of the radiocarbon date and to adjustments of the calibration curve. Other methods give more stable results. The weighted average of the probability distribution function is recommended as the best central-point estimate, but more consideration should be given to using the full probability distribution rather than a point estimate in developing age-depth models.

381 citations

Journal ArticleDOI
TL;DR: A family of probability densities, which has proved useful in modelling the size distributions of various phenomens, including incomes and earnings, human settlement sizes, oil-field volumes and particle sizes, is introduced.
Abstract: A family of probability densities, which has proved useful in modelling the size distributions of various phenomens, including incomes and earnings, human settlement sizes, oil-field volumes and particle sizes, is introduced. The distribution, named herein as the double Pareto-lognormal or dPlN distribution, arises as that of the state of a geometric Brownian motion (GBM), with lognormally distributed initial state, after an exponentially distributed length of time (or equivalently as the distribution of the killed state of such a GBM with constant killing rate). A number of phenomena can be viewed as resulting from such a process (e.g., incomes, settlement sizes), which explains the good fit. Properties of the distribution are derived and estimation methods discussed. The distribution exhibits Paretian power-law) behaviour in both tails, and when plotted on logarithmic axes, its density exhibits hyperbolic-type behaviour.

379 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022906
2021906
20201,047
20191,117
20181,083