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Journal articles on the topic 'Probability density function'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

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

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2

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 clea

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3

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

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4

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

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5

Ben Nakhi, Y., and S. L. Kalla. "A generalized beta function and associated probability density." International Journal of Mathematics and Mathematical Sciences 30, no. 8 (2002): 467–78. http://dx.doi.org/10.1155/s0161171202007512.

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We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are derived. Some special cases are mentioned. Some figures for pdf, hazard rate function, and mean residue life function are given. These figures reflect the role of shape and scale parameters.

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6

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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7

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

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8

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

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9

Chen, Zhicheng, Yuequan Bao, Hui Li, and Billie F. Spencer. "A novel distribution regression approach for data loss compensation in structural health monitoring." Structural Health Monitoring 17, no. 6 (2017): 1473–90. http://dx.doi.org/10.1177/1475921717745719.

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Structural health monitoring has arisen as an important tool for managing and maintaining civil infrastructure. A critical problem for all structural health monitoring systems is data loss or data corruption due to sensor failure or other malfunctions, which bring into question in subsequent structural health monitoring data analysis and decision-making. Probability density functions play a very important role in many applications for structural health monitoring. This article focuses on data loss compensation for probability density function estimation in structural health monitoring using im

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10

Martinez, Alexandre Souto, Rodrigo Silva González, and César Augusto Sangaletti Terçariol. "Generalized Probability Functions." Advances in Mathematical Physics 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/206176.

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From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs). A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the ge

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11

Tarasov, Vasily E. "Nonlocal Probability Theory: General Fractional Calculus Approach." Mathematics 10, no. 20 (2022): 3848. http://dx.doi.org/10.3390/math10203848.

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Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of the general fractional calculus in the Luchko form is proposed. Some basic concepts of the nonlocal probability theory are proposed, including nonlocal (general fractional) generalizations of probability density, cumulative distribution functions, probability, average values, and characteristic functions. Nonlocality is described by the pairs of

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12

Kim, Dojin, Lee-Chae Jang, Seongook Heo, and Patcharee Wongsason. "Note on fuzzifying probability density function and its properties." AIMS Mathematics 8, no. 7 (2023): 15486–98. http://dx.doi.org/10.3934/math.2023790.

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<abstract><p>This paper applies the concepts of fuzzifying functions to the probability density function of a random variable and introduce a fuzzifying probability to better understand the probability arising from the uncertainties of the probability density function. Using the fuzzifying probability, we derive the fuzzifying expected value and the fuzzifying variance of a random variable with the fuzzifying probability density function. Additionally, we provide examples of a fuzzifying probability density function to validate that the proposed fuzzy concepts generalize crisp expe

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13

Cox, Nicholas J. "Speaking Stata: Density Probability Plots." Stata Journal: Promoting communications on statistics and Stata 5, no. 2 (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 a

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14

Ateia, Khalid A., and Tarig A. Abdelhaleem. "Appropriate Probability Density Function of Convex Bodies." Journal of The Faculty of Science and Technology, no. 6 (January 13, 2021): 130–39. http://dx.doi.org/10.52981/jfst.vi6.619.

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We investigate under the notion of Large Deviation Principle & Concentration of Measure as a technique,the ability of estimating the probability density function of any random vector in the space Rn. We found that an appropriate probability distribution for any convex body in the space is sub – Gaussian.

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15

Derksen, R. W., P. J. Sullivan, and H. Yip. "Asymptotic probability density function of a scalar." AIAA Journal 32, no. 5 (1994): 1083–84. http://dx.doi.org/10.2514/3.12099.

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16

Watkins, Alan H. "Integrating the Standard Normal Probability Density Function." Teaching Statistics 15, no. 2 (1993): 49. http://dx.doi.org/10.1111/j.1467-9639.1993.tb00267.x.

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17

Aldershof, B., J. S. Marron, B. U. Park, and M. P. Wand. "Facts about the gaussian probability density function." Applicable Analysis 59, no. 1-4 (1995): 289–306. http://dx.doi.org/10.1080/00036819508840406.

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18

Pyati, V. P. "An exponential second-order probability-density function." Proceedings of the IEEE 75, no. 11 (1987): 1548–49. http://dx.doi.org/10.1109/proc.1987.13921.

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19

Mordant, N., A. M. Crawford, and E. Bodenschatz. "Experimental Lagrangian acceleration probability density function measurement." Physica D: Nonlinear Phenomena 193, no. 1-4 (2004): 245–51. http://dx.doi.org/10.1016/j.physd.2004.01.041.

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20

Kapitaniak, T. "Quantifying chaos with amplitude probability density function." Journal of Sound and Vibration 114, no. 3 (1987): 588–92. http://dx.doi.org/10.1016/s0022-460x(87)80026-3.

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21

Chen, Song Xi. "Probability Density Function Estimation Using Gamma Kernels." Annals of the Institute of Statistical Mathematics 52, no. 3 (2000): 471–80. http://dx.doi.org/10.1023/a:1004165218295.

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22

Vilar, E., and T. J. Moulsley. "Comment: Probability density function of amplitude scintillations." Electronics Letters 21, no. 14 (1985): 620. http://dx.doi.org/10.1049/el:19850438.

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23

Ortgies, G. "Reply: Probability density function of amplitude scintillations." Electronics Letters 21, no. 14 (1985): 621. http://dx.doi.org/10.1049/el:19850439.

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24

Ortgies, G. "Erratum: Probability density function of amplitude scintillations." Electronics Letters 21, no. 14 (1985): 632. http://dx.doi.org/10.1049/el:19850447.

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25

BALÁZS, FERENC, and SÁNDOR IMRE. "QUANTUM COMPUTATION BASED PROBABILITY DENSITY FUNCTION ESTIMATION." International Journal of Quantum Information 03, no. 01 (2005): 93–98. http://dx.doi.org/10.1142/s0219749905000578.

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Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least the probability density function (PDF), which to estimate is classically a time consumpting and/or less accurate hard task that may make decisions to fail. This paper describes the design of a quantum assisted PDF estimation method also by way of an example, which promises to achieve the exact PDF by proper setting of parameters in a very rapid way.

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26

XING, YI-FAN, and JUN WU. "PROBABILITY DENSITY FUNCTION CONTROL OF QUANTUM SYSTEMS." International Journal of Modern Physics B 25, no. 17 (2011): 2289–97. http://dx.doi.org/10.1142/s0217979211101089.

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This paper proposes a new method of controlling quantum systems via probability density function (PDF) control. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed for the general case and limited input energy, respectively. Unlike traditional quantum control methods, this method directly controls the probability distribution of the quantum state. It provides an alternative method for quantum control engineering.

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27

FIORI, SIMONE. "PROBABILITY DENSITY FUNCTION LEARNING BY UNSUPERVISED NEURONS." International Journal of Neural Systems 11, no. 05 (2001): 399–417. http://dx.doi.org/10.1142/s0129065701000898.

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In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation method

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28

Yano, Jun-Ichi. "Prognostic assumed-probability-density-function (distribution density function) approach: further generalization and demonstrations." Nonlinear Processes in Geophysics 31, no. 3 (2024): 359–80. http://dx.doi.org/10.5194/npg-31-359-2024.

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Abstract. A methodology for directly predicting the time evolution of the assumed parameters for distribution densities based on the Liouville equation, as proposed earlier, is extended to multidimensional cases and to cases in which the systems are constrained by integrals over a part of the variable range. The general formulation developed here is applicable to a wide range of problems, including the frequency distributions of subgrid-scale variables, hydrometeor size distributions, and probability distributions characterizing data uncertainties. The extended methodology is tested against a

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29

ARAKAWA, Hiroyuki, Shigeru INAGAKI, Yoshihiko NAGASHIMA, et al. "Probability Density Function of Density Fluctuations in Cylindrical Helicon Plasmas." Plasma and Fusion Research 5 (2010): S2044. http://dx.doi.org/10.1585/pfr.5.s2044.

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30

Fang, Lingling, and Yunxia Zhang. "Probability Density Function Analysis Based on Logistic Regression Model." International Journal of Circuits, Systems and Signal Processing 16 (January 5, 2022): 60–69. http://dx.doi.org/10.46300/9106.2022.16.9.

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The data fitting level in probability density function analysis has great influence on the analysis results, so it is of great significance to improve the data fitting level. Therefore, a probability density function analysis method based on logistic regression model is proposed. The logistic regression model with kernel function is established, and the optimal window width and mean square integral error are selected to limit the solution accuracy of probability density function. Using the real probability density function, the probability density function with the smallest error is obtained.

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31

Hielscher, R., H. Schaeben, and D. Chateigner. "On the entropy to texture index relationship in quantitative texture analysis." Journal of Applied Crystallography 40, no. 2 (2007): 371–75. http://dx.doi.org/10.1107/s0021889806055476.

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This communication demonstrates a sharp inequality between the L^{2}-norm and the entropy of probability density functions. This inequality is applied to texture analysis, and the relationship between the entropy and the texture index of an orientation density function is characterized. More precisely, the orientation space is shown to allow for texture index and entropy variations of orientation probability density functions between an upper and a lower bound for the entropy. In this way, it is proved that there is no functional relationship between entropy and texture index of an orientation

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32

Markovich, Liubov A., Justus Urbanetz, and Vladimir I. Man’ko. "Not All Probability Density Functions Are Tomograms." Entropy 26, no. 3 (2024): 176. http://dx.doi.org/10.3390/e26030176.

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This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful whe

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33

Cartinhour, Jack. "One-dimensional marginal density functions of a truncated multivariate normal density function." Communications in Statistics - Theory and Methods 19, no. 1 (1990): 197–203. http://dx.doi.org/10.1080/03610929008830197.

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34

Er, G. K. "The Probabilistic Solutions to Nonlinear Random Vibrations of Multi-Degree-of-Freedom Systems." Journal of Applied Mechanics 67, no. 2 (1999): 355–59. http://dx.doi.org/10.1115/1.1304842.

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The probability density function of the responses of nonlinear random vibration of a multi-degree-of-freedom system is formulated in the defined domain as an exponential function of polynomials in state variables. The probability density function is assumed to be governed by Fokker-Planck-Kolmogorov (FPK) equation. Special measure is taken to satisfy the FPK equation in the average sense of integration with the assumed function and quadratic algebraic equations are obtained for determining the unknown probability density function. Two-degree-of-freedom systems are analyzed with the proposed me

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35

Hussain, Mohammad Rashid, Mohammed Qayyum, and Mohammad Equebal Hussain. "Transportation Problem of LPP Involving Probability Density Function." International Journal of Recent Contributions from Engineering, Science & IT (iJES) 7, no. 1 (2019): 42. http://dx.doi.org/10.3991/ijes.v7i1.9909.

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<p>In Linear Programming Problem (LPP), Transportation Problem (TP) is an application which is used to optimize through the probability density function of statistical approach. The main objective of this paper is to reduce complexity in Maximization problem of LPP, by fulfilling the relation between the objective function and constraints with the largest value. Here, we used non-negative integer and complex number of linear combination of form x<sup>m</sup>e<sup>λx</sup>. It has been decided with reasonably great probability, decision region, fundamental probabil

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36

La Valle, Gabriele, Rossella Laudani, and Giovanni Falsone. "Response probability density function for non-bijective transformations." Communications in Nonlinear Science and Numerical Simulation 107 (April 2022): 106190. http://dx.doi.org/10.1016/j.cnsns.2021.106190.

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37

Jacobs, Donald. "Best Probability Density Function for Random Sampled Data." Entropy 11, no. 4 (2009): 1001–24. http://dx.doi.org/10.3390/e11041001.

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38

Petrushin, Vladimir N., Evgeny V. Nikulchev, and Dmitry A. Korolev. "Histogram arithmetic under uncertainty of probability density function." Applied Mathematical Sciences 9 (2015): 7043–52. http://dx.doi.org/10.12988/ams.2015.510644.

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39

Lira, I. "The generalized maximum entropy trapezoidal probability density function." Metrologia 45, no. 4 (2008): L17—L20. http://dx.doi.org/10.1088/0026-1394/45/4/n01.

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40

Srikanth, M., H. K. Kesavan, and P. H. Roe. "Probability density function estimation using the MinMax measure." IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 30, no. 1 (2000): 77–83. http://dx.doi.org/10.1109/5326.827456.

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41

Wöger, W. "Information-Based Probability Density Function for a Quantity." Measurement Techniques 46, no. 9 (2003): 815–23. http://dx.doi.org/10.1023/b:mete.0000008438.11627.3f.

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42

Zhao, Hui, Yisong Zhang, Pedram Khalili Amiri, et al. "Spin-Torque Driven Switching Probability Density Function Asymmetry." IEEE Transactions on Magnetics 48, no. 11 (2012): 3818–20. http://dx.doi.org/10.1109/tmag.2012.2197815.

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43

Vladimirovich Guryev, Marat. "Wave Function Is not Amplitude of Probability Density." American Journal of Modern Physics 6, no. 4 (2017): 49. http://dx.doi.org/10.11648/j.ajmp.20170604.11.

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44

Lagnoux, Agnès, Sabine Mercier, and Pierre Vallois. "Probability density function of the local score position." Stochastic Processes and their Applications 129, no. 10 (2019): 3664–89. http://dx.doi.org/10.1016/j.spa.2018.10.008.

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45

Hsu, A. t., and G. B. He. "Probability density function method for turbulent hydrogen flames." International Journal of Hydrogen Energy 24, no. 1 (1999): 65–74. http://dx.doi.org/10.1016/s0360-3199(98)00032-9.

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46

Hsu, A. T., and G. B. He. "Probability-density function model of turbulent hydrogen flames." Applied Energy 67, no. 1-2 (2000): 117–35. http://dx.doi.org/10.1016/s0306-2619(00)00009-x.

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47

López-Rubio, Ezequiel, and Juan Miguel Ortiz-de-Lazcano-Lobato. "Soft clustering for nonparametric probability density function estimation." Pattern Recognition Letters 29, no. 16 (2008): 2085–91. http://dx.doi.org/10.1016/j.patrec.2008.07.010.

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48

Di Cera, E., and Z. Q. Chen. "The binding capacity is a probability density function." Biophysical Journal 65, no. 1 (1993): 164–70. http://dx.doi.org/10.1016/s0006-3495(93)81033-6.

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49

Dimitrov, Nedialko B., and Valentin T. Jordanov. "Probability Density Function Transformation Using Seeded Localized Averaging." IEEE Transactions on Nuclear Science 59, no. 4 (2012): 1300–1308. http://dx.doi.org/10.1109/tns.2011.2177861.

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50

Ho, Keang-Po, and Joseph M. Kahn. "Exact probability-density function for phase-measurement interferometry." Journal of the Optical Society of America A 12, no. 9 (1995): 1984. http://dx.doi.org/10.1364/josaa.12.001984.

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