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Автор: Grafiati

Опубліковано: 8 червня 2024

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1

Riopel, Martin, Jean Bégin, and Jean-Claude Ruel. "Probabilités de pertes des tiges individuelles, cinq ans après des coupes avec protection des petites tiges marchandes, dans des forêts résineuses du Québec." Canadian Journal of Forest Research 40, no. 7 (July 2010): 1458–72. http://dx.doi.org/10.1139/x10-059.

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La coupe avec protection des petites tiges marchandes est un type de coupe partielle qui consiste généralement à récolter toutes les tiges d’un diamètre à hauteur de poitrine (dhp) supérieur à 15,0 cm, tout en conservant les tiges de plus petites dimensions. Le succès du traitement, appliqué à des forêts résineuses mûres dominées par le sapin baumier ( Abies balsamea (L.) Mill.) ou l’épinette noire ( Picea mariana (Mill.) Britton, Sterns & Poggenb.), repose en partie sur la capacité des tiges protégées à survivre. Un modèle logistique mixte a été calibré à partir de 27 blocs expérimentaux établis au Québec. Ce modèle identifie les variables qui conditionnent les probabilités de pertes des tiges individuelles protégées de 5,1 cm et plus de dhp, par mortalité sur pied ou par chablis, 5 ans après des coupes avec protection des petites tiges marchandes. Les résultats indiquent que les probabilités de pertes après traitement sont largement tributaires des caractéristiques du peuplement avant coupe (surface terrière marchande, densité de gaules, proportion de pin gris ( Pinus banksiana Lamb.)), de la qualité des opérations (procédé de récolte, taux de protection des petites tiges marchandes) et des caractéristiques des tiges protégées au moment de la coupe (inclinaison, dhp, essence). Les variables associées à l’exposition aux vents et à l’écologie des stations n’ont pas permis d’améliorer le modèle. Afin d’éviter des pertes trop élevées, il importe de bien cibler les peuplements à traiter et de réaliser un suivi rigoureux des opérations de récolte.

2

Ouimet, Marc, and Pierre Tremblay. "Trajets urbains et risques de victimisation : les sites de transit et le cas du métro de Montréal." Criminologie 34, no. 1 (October 2, 2002): 157–76. http://dx.doi.org/10.7202/004759ar.

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Résumé Les acteurs urbains sont généralement en mouvement et cessent de l'être seulement lorsque leurs activités exigent d'eux qu'ils demeurent stationnaires pour un intervalle de temps limité. Leurs parcours, composé de sommets (destinations) reliés entre eux par des chemins, forme un circuit, chaque trajectoire ramenant le plus souvent la personne qui se déplace à son point d'origine. Nous analysons la distribution des probabilités individuelles de victimisation personnelle associées aux diverses destinations qui définissent ce parcours (lieux de magasinage, de loisir, de vie domestique et de travail) et ses lieux intercalaires de transit (« la rue », le métro et les autobus). Cette analyse, basée sur les délits rapportés à la police à Montréal en 1995, prend en considération la distribution de la densité, variable selon les sites urbains, des occasions de contacts interpersonnels et propose une évaluation des risques individuels de victimisation auxquels sont exposés les usagers du métro.

3

Assis, Janilson Pinheiro, Roberto Pequeno de Sousa, Bem Deivid de Oliveira Batista, and Paulo César Ferreira Linhares. "Probabilidade de chuva em Piracicaba, SP, através da distribuição densidade de probabilidade Gama." Revista Brasileira de Geografia Física 11, no. 2 (2018): 814–25. http://dx.doi.org/10.26848/rbgf.v10.6.p814-825.

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4

Assis, Janilson Pinheiro, Roberto Pequeno de Sousa, Bem Deivid de Oliveira Batista, and Paulo César Ferreira Linhares. "Probabilidade de chuva em Piracicaba, SP, através da distribuição densidade de probabilidade Gama." Revista Brasileira de Geografia Física 11, no. 3 (2018): 814–25. http://dx.doi.org/10.26848/rbgf.v11.3.p814-825.

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5

Farmer, Jenny, Eve Allen, and Donald J. Jacobs. "Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities." Mathematics 11, no. 1 (December 28, 2022): 155. http://dx.doi.org/10.3390/math11010155.

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Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 106 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

6

Bian Chenshu, 边宸舒, 刘元坤 Liu Yuankun та 于馨 Yu Xin. "基于概率密度函数的彩色相位测量轮廓术校正". Acta Optica Sinica 42, № 7 (2022): 0712002. http://dx.doi.org/10.3788/aos202242.0712002.

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7

Jones, M. C., and F. Daly. "Density probability plots." Communications in Statistics - Simulation and Computation 24, no. 4 (January 1995): 911–27. http://dx.doi.org/10.1080/03610919508813284.

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8

Xiao, Yongshun. "THE MARGINAL PROBABILITY DENSITY FUNCTIONS OF WISHART PROBABILITY DENSITY FUNCTION." Far East Journal of Theoretical Statistics 54, no. 3 (May 1, 2018): 239–326. http://dx.doi.org/10.17654/ts054030239.

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9

Lin, Yi-Shin, Andrew Heathcote, and William R. Holmes. "Parallel probability density approximation." Behavior Research Methods 51, no. 6 (August 30, 2019): 2777–99. http://dx.doi.org/10.3758/s13428-018-1153-1.

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10

Amonmidé, Isidore, Germain D. Fayalo, and Gustave D. Dagbenonbakin. "Effet de la période et densité de semis sur la croissance et le rendement du cotonnier au Bénin." Journal of Applied Biosciences 152 (August 31, 2020): 15676–97. http://dx.doi.org/10.35759/jabs.152.7.

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Objectif : L’objectif de l’étude était d’identifier les meilleures périodes et densités de semis dans les différentes zones agro-écologiques cotonnières du Bénin dans un contexte de changement climatique. Méthodologie et résultats : Les expérimentations ont été conduites pendant deux ans (2017 et 2018) en station au Bénin dans un dispositif expérimental en split-plot à deux facteurs, la période (facteur principal) et la densité de semis (facteur secondaire) respectivement à quatre et cinq variantes avec quatre répétitions. Les données collectées ont été soumises à une analyse de variance sous le logiciel R.3.6.1 au seuil de 5% de probabilité d’erreur. Les résultats ont montré au cours des deux années d’expérimentation que les semis tardifs ont enregistré les plus faibles rendements en coton graine dans la zone centre-nord tandis que toutes les dates de semis ont donné des rendements équivalents dans la zone nord. La densité de semis à 62500 plants/ha a donné le meilleur rendement. Conclusion et applications des résultats : Le semis du cotonnier peut s’étendre sur quatre décades (20 mai au 30 juin) dans la zone nord contrairement au centre-nord où la période optimale de semis s’étend seulement sur les deux dernières décades de juin (10-30 juin). La densité à 62500 plants/ha (0,20m x 0,80m à 1 plant/poquet) pourrait être recommandée pour l’amélioration des rendements en culture cotonnière au Bénin. L’adoption de cette densité de semis offre aux producteurs l’opportunité de mécaniser les opérations de semis et de fertilisation, compte tenu de la faible distance inter-poquets par rapport aux densités en vulgarisation. Mots clés : Période de semis, densité de semis, rendement coton graine, zones cotonnières, Bénin. Effect of sowing time and plant density on growth, development and yield in Benin ABSTRACT Objective: This study aimed at identifying the best sowing date and plant densities in the different cotton agro-ecological zones of Benin in a context of climate change. Methodology and results: On-station trials were conducted during two years (2017 and 2018) in Benin in a split-plot experimental design with two factors, the sowing date (main factor) and the plant density (secondary factor) with four and five levels, respectively with four replications. Collected data were submitted to an analysis of variance under R.3.6.1 software at 5% probability threshold error. Results showed other the two Amonmidé et al., J. Appl. Biosci. 2020 Effet de la période et densité de semis sur la croissance et le rendement du cotonnier au Bénin 15677 years of trial that late sowings recorded the lowest cotton seed yields in the northern central zone while all sowing date gave similar yields in the northern zone. Planting density of 62500 plants/ha gave the best yields. Conclusion and applications of the results: Cotton sowing could be extended over four decades (20 May to 30 June) in the northern zone contrarily to the northern central zone where the optimal sowing time covers only the last two decades of June (10-30 June). Plant density of 62500 plants/ha (0.20 m x 0.80 m at 1 plant/pot) could be recommended to improve cotton seed yields in Benin. The adoption of this new plant density offers producers the opportunity to mechanize sowing and fertilizer application, given low inter-plant space compared to the recommendation in Benin. Key words: Sowing date, plant density, cotton seed yield, cotton agro-ecological zones, Benin.

11

Zhong-hua, Liu, Chen Li-hua, and Zhu You-xing. "Probability Density and Joint Probability Density of SDE with General Nonlinear Gaussian Noise." Communications in Theoretical Physics 13, no. 2 (March 1990): 135–46. http://dx.doi.org/10.1088/0253-6102/13/2/135.

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12

Carta, Lynn, and David Carta. "Nematode specific gravity profiles and applications to flotation extraction and taxonomy." Nematology 2, no. 2 (2000): 201–10. http://dx.doi.org/10.1163/156854100508935.

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AbstractA technique is described that refines the standard sugar flotation procedure used to isolate nematodes from their surroundings. By centrifuging nematodes in a number of increasing specific gravity solutions and plotting the fraction floating, the cumulative probability distribution of the population’s specific gravity is generated. By assuming normality, the population mean, μ, and standard deviation, σ, are found by a nonlinear least squares procedure. These density parameters along with their error covariance matrix may be used as a taxonomic physical character. A chi-squared test is derived for comparing populations. Mean and standard deviation pairs (μ, σ) were found for the specific gravities of the adult stage of the plant parasites Pratylenchus agilis (1.068, 0.017), P. scribneri (1.073, 0.028), P. penetrans (1.058, 0.008) and the bacterial-feeder Caenorhabditis elegans (1.091, 0.016). La technique exposée affine le procédure standard par flottation au sucre utilisée pour séparer les nématodes de leur milieu. La centrifugation des nématodes dans une série de solutions de densités spécifiques et la mise en diagramme de la valeur de la fraction surnageante permettent de connaître le répartition de la probabilité cumulée de la densité spécifique de la population en cause. La normalité étant supposée, la moyenne de la population, μ, et la déviation standard, σ, sont calculées par la méthode des moindres carrés non linéaires. Ces paramètres relatifs à la densité ainsi que leur matrice de co-variance d’erreur peuvent être utilisés en taxinomie comme caractère physique. Un test chi2 en est dérivé pour comparer les populations entre elles. Des données en paires — moyenne (μ) et écart-type (σ) — ont été définies pour les densités des adultes des espèces phytoparasites Pratylenchus agilis (1,068; 0,017), P. scribneri (1,073; 0,028), P. penetrans (1,058; 0,008), ainsi que pour l’espèce bactérivore Caenorhabditis elegans (1,091; 0,016).

13

Kohnle, Antje, Alexander Jackson, and Mark Paetkau. "The Difference Between a Probability and a Probability Density." Physics Teacher 57, no. 3 (March 2019): 190–92. http://dx.doi.org/10.1119/1.5092484.

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14

Anju, Dr Vineeta Basotia, and Dr Ritikesh Kumar. "Analysis on Probability Mass Function and Probability Density Function." Irish Interdisciplinary Journal of Science & Research 08, no. 01 (2024): 08–12. http://dx.doi.org/10.46759/iijsr.2024.8102.

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Probability Mass Function (PMF) and Probability Density Function (PDF) are fundamental concepts in probability theory and statistics that play a crucial role in describing the probability distribution of random variables. This abstract provides a comprehensive overview of these concepts, highlighting their definitions, characteristics, and applications. The Probability Mass Function is a concept primarily associated with discrete random variables. It defines the probability of a specific outcome occurring. The PMF assigns probabilities to individual values in the sample space, providing a clear picture of the likelihood of each possible outcome. Commonly denoted as P(X=x), where X is the random variable and x is a specific value, the PMF must satisfy two essential properties: non-negativity and the sum of probabilities over all possible outcomes equals one. On the other hand, the Probability Density Function is a concept applied to continuous random variables. Unlike the PMF, which deals with specific values, the PDF deals with ranges of values. The PDF represents the probability that a continuous random variable falls within a given interval. Denoted as f(x), it is essential to note that the probability of any specific point is zero, and instead, probabilities are defined for intervals. The area under the PDF curve over a given interval corresponds to the probability of the random variable falling within that interval. Understanding the differences and similarities between PMF and PDF is crucial for statistical analysis. While PMF is discrete and deals with specific values, PDF is continuous and provides probabilities for intervals. Both functions are integral to the calculation of various statistical measures, including expected values, variance, and standard deviation. This abstract concludes with a discussion of practical applications in diverse fields, such as finance, engineering, and natural sciences, where a deep understanding of PMF and PDF is essential for making informed decisions and drawing meaningful conclusions from data. The integration of these concepts into statistical models and analyses enhances the accuracy and reliability of predictions, making PMF and PDF indispensable tools in the field of probability and statistics

15

Rigollet, Philippe. "Inégalités d'oracle pour l'estimation d'une densité de probabilité." Comptes Rendus Mathematique 340, no. 1 (January 2005): 59–62. http://dx.doi.org/10.1016/j.crma.2004.11.009.

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16

Maschio, Samuele. "Natural density and probability, constructively." Reports on Mathematical Logic 55 (2020): 41–59. http://dx.doi.org/10.4467/20842589rm.20.002.12434.

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17

Koliander, Gunther, Yousef El-Laham, Petar M. Djuric, and Franz Hlawatsch. "Fusion of Probability Density Functions." Proceedings of the IEEE 110, no. 4 (April 2022): 404–53. http://dx.doi.org/10.1109/jproc.2022.3154399.

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18

Abdul-al, Khaled I., and J. L. Geluk. "ON SMOOTHED PROBABILITY DENSITY ESTIMATION." Bulletin of informatics and cybernetics 23, no. 3/4 (March 1989): 199–208. http://dx.doi.org/10.5109/13406.

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19

Kakizawa, Yoshihide. "Bernstein polynomial probability density estimation." Journal of Nonparametric Statistics 16, no. 5 (October 2004): 709–29. http://dx.doi.org/10.1080/1048525042000191486.

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20

Minotti, F. O., and C. Ferro Fontán. "Navier-stokes probability density function." European Journal of Mechanics - B/Fluids 17, no. 4 (July 1998): 505–18. http://dx.doi.org/10.1016/s0997-7546(98)80007-1.

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21

Waissi, Gary R. "A unifying probability density function." Applied Mathematics Letters 6, no. 5 (September 1993): 25–26. http://dx.doi.org/10.1016/0893-9659(93)90093-3.

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22

Rosenbrock, H. H. "The quantum-mechanical probability density." Physics Letters A 116, no. 9 (July 1986): 410–12. http://dx.doi.org/10.1016/0375-9601(86)90370-1.

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23

Cox, Nicholas J. "Speaking Stata: Density Probability Plots." Stata Journal: Promoting communications on statistics and Stata 5, no. 2 (June 2005): 259–73. http://dx.doi.org/10.1177/1536867x0500500210.

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Density probability plots show two guesses at the density function of a continuous variable, given a data sample. The first guess is the density function of a specified distribution (e.g., normal, exponential, gamma, etc.) with appropriate parameter values plugged in. The second guess is the same density function evaluated at quantiles corresponding to plotting positions associated with the sample's order statistics. If the specified distribution fits well, the two guesses will be close. Such plots, suggested by Jones and Daly in 1995, are explained and discussed with examples from simulated and real data. Comparisons are made with histograms, kernel density estimation, and quantile–quantile plots.

24

Stephens, M. E., B. W. Goodwin, and T. H. Andres. "Deriving parameter probability density functions." Reliability Engineering & System Safety 42, no. 2-3 (January 1993): 271–91. http://dx.doi.org/10.1016/0951-8320(93)90094-f.

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25

Ashby, F. Gregory, and Leola A. Alfonso-Reese. "Categorization as Probability Density Estimation." Journal of Mathematical Psychology 39, no. 2 (June 1995): 216–33. http://dx.doi.org/10.1006/jmps.1995.1021.

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26

McIntyre, T., T. L. Majelantle, D. J. Slip, and R. G. Harcourt. "Quantifying imperfect camera-trap detection probabilities: implications for density modelling." Wildlife Research 47, no. 2 (2020): 177. http://dx.doi.org/10.1071/wr19040.

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Abstract ContextData obtained from camera traps are increasingly used to inform various population-level models. Although acknowledged, imperfect detection probabilities within camera-trap detection zones are rarely taken into account when modelling animal densities. AimsWe aimed to identify parameters influencing camera-trap detection probabilities, and quantify their relative impacts, as well as explore the downstream implications of imperfect detection probabilities on population-density modelling. MethodsWe modelled the relationships between the detection probabilities of a standard camera-trap model (n=35) on a remotely operated animal-shaped soft toy and a series of parameters likely to influence it. These included the distance of animals from camera traps, animal speed, camera-trap deployment height, ambient temperature (as a proxy for background surface temperatures) and animal surface temperature. We then used this detection-probability model to quantify the likely influence of imperfect detection rates on subsequent population-level models, being, in this case, estimates from random encounter density models on a known density simulation. Key resultsDetection probabilities mostly varied predictably in relation to measured parameters, and decreased with an increasing distance from the camera traps and speeds of movement, as well as heights of camera-trap deployments. Increased differences between ambient temperature and animal surface temperature were associated with increased detection probabilities. Importantly, our results showed substantial inter-camera (of the same model) variability in detection probabilities. Resulting model outputs suggested consistent and systematic underestimation of true population densities when not taking imperfect detection probabilities into account. ConclusionsImperfect, and individually variable, detection probabilities inside the detection zones of camera traps can compromise resulting population-density estimates. ImplicationsWe propose a simple calibration approach for individual camera traps before field deployment and encourage researchers to actively estimate individual camera-trap detection performance for inclusion in subsequent modelling approaches.

27

Jamieson, L. E., and S. P. Brooks. "Density dependence in North American ducks." Animal Biodiversity and Conservation 27, no. 1 (June 1, 2004): 113–28. http://dx.doi.org/10.32800/abc.2004.27.0113.

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The existence or otherwise of density dependence within a population can have important implications for the management of that population. Here, we use estimates of abundance obtained from annual aerial counts on the major breeding grounds of a variety of North American duck species and use a state space model to separate the observation and ecological system processes. This state space approach allows us to impose a density dependence structure upon the true underlying population rather than on the estimates and we demonstrate the improved robustness of this procedure for detecting density dependence in the population. We adopt a Bayesian approach to model fitting, using Markov chain Monte Carlo (MCMC) methods and use a reversible jump MCMC scheme to calculate posterior model probabilities which assign probabilities to the presence of density dependence within the population, for example. We show how these probabilities can be used either to discriminate between models or to provide model-averaged predictions which fully account for both parameter and model uncertainty.

28

Mejia, Hannah, and Jay Pulliam. "P‐ and T‐Axis Probabilities (PaTaPs): Characterizing Regional Stress Patterns with Probability Density Functions of Fault‐Plane Uncertainties." Seismological Research Letters 89, no. 6 (August 22, 2018): 2354–61. http://dx.doi.org/10.1785/0220180112.

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29

Norets, Andriy, and Justinas Pelenis. "POSTERIOR CONSISTENCY IN CONDITIONAL DENSITY ESTIMATION BY COVARIATE DEPENDENT MIXTURES." Econometric Theory 30, no. 3 (November 18, 2013): 606–46. http://dx.doi.org/10.1017/s026646661300042x.

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This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel stick-breaking processes for modeling the mixing probabilities. We show that the posterior in these two models is weakly and strongly consistent for a large class of data-generating processes. A simulation study conducted in the paper demonstrates that the models can perform well in small samples.

30

Joachim, C. "The probability and energy density currents as density functionals." Journal of Physics A: Mathematical and General 19, no. 13 (September 11, 1986): 2549–57. http://dx.doi.org/10.1088/0305-4470/19/13/020.

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31

Delgado, V. "Quantum probability distribution of arrival times and probability current density." Physical Review A 59, no. 2 (February 1, 1999): 1010–20. http://dx.doi.org/10.1103/physreva.59.1010.

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32

Ooi, Hong, and Peter Hall. "Attributing a probability to the shape of a probability density." Annals of Statistics 32, no. 5 (October 2004): 2098–123. http://dx.doi.org/10.1214/009053604000000607.

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33

LIAN, Feng, Chong-Zhao HAN, Wei-Feng LIU, and Xiang-Hui YUAN. "Multiple-model Probability Hypothesis Density Smoother." Acta Automatica Sinica 36, no. 7 (August 3, 2010): 939–50. http://dx.doi.org/10.3724/sp.j.1004.2010.00939.

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34

Kwasniok, Frank. "Semiparametric maximum likelihood probability density estimation." PLOS ONE 16, no. 11 (November 9, 2021): e0259111. http://dx.doi.org/10.1371/journal.pone.0259111.

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A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are estimated by global maximum likelihood without any roughness penalty. A statistically orthogonal formulation of the inference problem and a numerically stable and fast convex optimization algorithm for its solution are presented. Automatic model selection over the type and number of basis functions is performed with the Bayesian information criterion. The methodology can naturally be applied to densities supported on bounded, infinite or semi-infinite domains without boundary bias. Relationships to the truncated moment problem and the moment-constrained maximum entropy principle are discussed and a new theorem on the existence of solutions is contributed. The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and observation data sets. The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density in terms of the number of modes and bumps.

35

Vovan, Tai. "Cluster Width of probability Density functions." Intelligent Data Analysis 23, no. 2 (April 4, 2019): 385–405. http://dx.doi.org/10.3233/ida-173794.

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36

Amindavar, H., and J. A. Ritcey. "Pade approximations of probability density functions." IEEE Transactions on Aerospace and Electronic Systems 30, no. 2 (April 1994): 416–24. http://dx.doi.org/10.1109/7.272264.

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37

Reggiani, L., and G. Tartara. "Probability density functions of soft information." IEEE Communications Letters 6, no. 2 (February 2002): 52–54. http://dx.doi.org/10.1109/4234.984688.

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Gille, Sarah T., and Stefan G. Llewellyn Smith. "Velocity Probability Density Functions from Altimetry." Journal of Physical Oceanography 30, no. 1 (January 2000): 125–36. http://dx.doi.org/10.1175/1520-0485(2000)030<0125:vpdffa>2.0.co;2.

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39

Miller, Gad, and David Horn. "Probability Density Estimation Using Entropy Maximization." Neural Computation 10, no. 7 (October 1, 1998): 1925–38. http://dx.doi.org/10.1162/089976698300017205.

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Анотація:

We propose a method for estimating probability density functions and conditional density functions by training on data produced by such distributions. The algorithm employs new stochastic variables that amount to coding of the input, using a principle of entropy maximization. It is shown to be closely related to the maximum likelihood approach. The encoding step of the algorithm provides an estimate of the probability distribution. The decoding step serves as a generative mode, producing an ensemble of data with the desired distribution. The algorithm is readily implemented by neural networks, using stochastic gradient ascent to achieve entropy maximization.

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Campos Venuti, L., and P. Zanardi. "Probability density of quantum expectation values." Physics Letters A 377, no. 31-33 (October 2013): 1854–61. http://dx.doi.org/10.1016/j.physleta.2013.05.041.

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41

Arranz, F. J., F. Borondo, and R. M. Benito. "Probability density distributions in phase space." Journal of Molecular Structure: THEOCHEM 426, no. 1-3 (March 1998): 87–93. http://dx.doi.org/10.1016/s0166-1280(97)00314-x.

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42

Ortgies, G. "Probability density function of amplitude scintillations." Electronics Letters 21, no. 4 (1985): 141. http://dx.doi.org/10.1049/el:19850100.

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43

Campioni, Luca, and Paolo Vestrucci. "On system failure probability density function." Reliability Engineering & System Safety 92, no. 10 (October 2007): 1321–27. http://dx.doi.org/10.1016/j.ress.2006.09.002.

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44

Morad, Kamalaldin, William Y. Svrcek, and Ian McKay. "Probability density estimation using incomplete data." ISA Transactions 39, no. 4 (September 2000): 379–99. http://dx.doi.org/10.1016/s0019-0578(00)00016-1.

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45

Kay, S. "Model-based probability density function estimation." IEEE Signal Processing Letters 5, no. 12 (December 1998): 318–20. http://dx.doi.org/10.1109/97.735424.

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46

Farmer, Jenny, and Donald Jacobs. "High throughput nonparametric probability density estimation." PLOS ONE 13, no. 5 (May 11, 2018): e0196937. http://dx.doi.org/10.1371/journal.pone.0196937.

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47

Yanev, Toni K. "Probability density functions of vegetation indices." Acta Astronautica 26, no. 2 (February 1992): 85–91. http://dx.doi.org/10.1016/0094-5765(92)90049-o.

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48

Sithiravel, Rajiv, Xin Chen, Ratnasingham Tharmarasa, Bhashyam Balaji, and Thiagalingam Kirubarajan. "The Spline Probability Hypothesis Density Filter." IEEE Transactions on Signal Processing 61, no. 24 (December 2013): 6188–203. http://dx.doi.org/10.1109/tsp.2013.2284139.

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49

Mahler, R. P. S., Ba-Tuong Vo, and Ba-Ngu Vo. "Forward-Backward Probability Hypothesis Density Smoothing." IEEE Transactions on Aerospace and Electronic Systems 48, no. 1 (January 2012): 707–28. http://dx.doi.org/10.1109/taes.2012.6129665.

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50

Schikora, Marek, Amadou Gning, Lyudmila Mihaylova, Daniel Cremers, and Wolfgang Koch. "Box-particle probability hypothesis density filtering." IEEE Transactions on Aerospace and Electronic Systems 50, no. 3 (July 2014): 1660–72. http://dx.doi.org/10.1109/taes.2014.120238.

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