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Journal articles on the topic 'Distributions de possibilités'

Author: Grafiati

Published: 1 February 2025

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1

Ji, Lin Na, Feng Bao Yang, and Xiao Xia Wang. "A Possibility Estimation Model and its Application." Applied Mechanics and Materials 475-476 (December 2013): 423–27. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.423.

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Aiming at some uncertainty problems such as quality inspection of adhesive structure and risk assessment in the practical engineering application, a possibility estimation model is established. Firstly, according to the fuzziness, randomness and uncertainty of the measurement data, a transformation method of possibility distribution with non-single peak values and nonlinearity is proposed from probability density function. Secondly, for possibility distributions of measurement data of each sensor, a kind of possibility fusion rules is put forward, then the fusion distribution is estimated by the possibility mean. Finally the model is applied to the mechanical property estimation of adhesive structure, and the result forecasts the quality. The proposed model with strong applicability, not only provides convenience for the operations among possibility distributions, but also offers new ideas and new methods to deal with uncertain problems.

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2

Cao, Yongqiang, and Xiaofei Qu. "On possibility distribution." Fuzzy Sets and Systems 69, no. 2 (January 1995): 171–79. http://dx.doi.org/10.1016/0165-0114(94)00150-6.

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3

CAMPOS, LUIS M. DE, and JUAN F. HUETE. "MEASUREMENT OF POSSIBILITY DISTRIBUTIONS." International Journal of General Systems 30, no. 3 (January 2001): 309–46. http://dx.doi.org/10.1080/03081070108960711.

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4

Lesniewska-Choquet, Charles, Gilles Mauris, Abdourrahmane M. Atto, and Gregoire Mercier. "On Elliptical Possibility Distributions." IEEE Transactions on Fuzzy Systems 28, no. 8 (August 2020): 1631–39. http://dx.doi.org/10.1109/tfuzz.2019.2920803.

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5

Mauris, G. "Transformation of Bimodal Probability Distributions Into Possibility Distributions." IEEE Transactions on Instrumentation and Measurement 59, no. 1 (January 2010): 39–47. http://dx.doi.org/10.1109/tim.2009.2025687.

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6

Yager, Ronald R. "Q-projections on possibility distributions." IEEE Transactions on Systems, Man, and Cybernetics SMC-15, no. 6 (November 1985): 775–77. http://dx.doi.org/10.1109/tsmc.1985.6313461.

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7

Spott, Martin. "A theory of possibility distributions." Fuzzy Sets and Systems 102, no. 2 (March 1999): 135–55. http://dx.doi.org/10.1016/s0165-0114(97)00102-4.

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8

PAL, NIKHIL R., and THOMAS GEORGE. "METRIC STRUCTURES ON POSSIBILITY DISTRIBUTIONS." International Journal of General Systems 25, no. 4 (January 1997): 389–98. http://dx.doi.org/10.1080/03081079708945164.

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9

Hormozinejad, Farshin. "Two-stage test with possibility of rejection of decision." Asian-European Journal of Mathematics 09, no. 03 (August 2, 2016): 1650050. http://dx.doi.org/10.1142/s1793557116500509.

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The multiple statistical hypotheses two-stage testing with possibility of rejecting of decision to make choice between hypotheses concerning the pair of groups of probability distributions is considered such that in the first stage one group of distributions is distinguished and then in the second stage, the true distribution is denoted between mentioned group of probability distributions. Description of characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing with possibility of decision rejection and the matrix of optimal asymptotically interdependencies of all pairs of the error probability exponents or reliabilities are studied. The goal of research is to express the optimal functional relation between the reliabilities of LAO hypotheses testing by a pair of stages and to compare with the case of similar one-stage testing.

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10

Recasens, J., and J. Lawry. "Normalizing Possibility Distributions Using t-Norms." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 03 (June 2003): 343–60. http://dx.doi.org/10.1142/s0218488503002119.

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A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms. For a given fuzzy subset μ, the corresponding normalized fuzzy subset [Formula: see text] can be viewed as the distribution of μ conditioned on the (degree of) existence of its elements with maximal membership. From this view point we investigate the less specific normal fuzzy subset of X among the most similar fuzzy subsets to μ and the normal fuzzy subset generating the same fuzzy T-preorder as μ.

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11

Yager, Ronald R. "On the instantiation of possibility distributions." Fuzzy Sets and Systems 128, no. 2 (June 2002): 261–66. http://dx.doi.org/10.1016/s0165-0114(01)00206-8.

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12

Tanaka, Hideo, and Hisao Ishibuchi. "Evidence theory of exponential possibility distributions." International Journal of Approximate Reasoning 8, no. 2 (February 1993): 123–40. http://dx.doi.org/10.1016/0888-613x(93)90024-8.

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13

RAMER, ARTHUR. "CONFLUENT POSSIBILITY DISTRIBUTIONS AND THEIR REPRESENTATIONS." International Journal of General Systems 15, no. 3 (August 1989): 217–31. http://dx.doi.org/10.1080/03081078908935047.

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14

Bouchon, Bernadette. "Fuzzy inferences and conditional possibility distributions." Fuzzy Sets and Systems 23, no. 1 (July 1987): 33–41. http://dx.doi.org/10.1016/0165-0114(87)90098-4.

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15

Dubois, Didier, and Henri Prade. "Practical Methods for Constructing Possibility Distributions." International Journal of Intelligent Systems 31, no. 3 (September 28, 2015): 215–39. http://dx.doi.org/10.1002/int.21782.

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16

PRADE, HENRI, and RONALD R. YAGER. "ESTIMATIONS OF EXPECTEDNESS AND POTENTIAL SURPRISE IN POSSIBILITY THEORY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 02, no. 04 (December 1994): 417–28. http://dx.doi.org/10.1142/s021848859400033x.

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This note investigates how various ideas of "expectedness" can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying "I would not be surprised that…" before an event takes place, or by saying "I knew it" after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of possibility of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined.

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17

Lemoine, Derek M. "Climate Sensitivity Distributions Dependence on the Possibility that Models Share Biases." Journal of Climate 23, no. 16 (August 15, 2010): 4395–415. http://dx.doi.org/10.1175/2010jcli3503.1.

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Abstract Uncertainty about biases common across models and about unknown and unmodeled feedbacks is important for the tails of temperature change distributions and thus for climate risk assessments. This paper develops a hierarchical Bayes framework that explicitly represents these and other sources of uncertainty. It then uses models’ estimates of albedo, carbon cycle, cloud, and water vapor–lapse rate feedbacks to generate posterior probability distributions for feedback strength and equilibrium temperature change. The posterior distributions are especially sensitive to prior beliefs about models’ shared structural biases: nonzero probability of shared bias moves some probability mass toward lower values for climate sensitivity even as it thickens the distribution’s positive tail. Obtaining additional models of these feedbacks would not constrain the posterior distributions as much as narrowing prior beliefs about shared biases or, potentially, obtaining feedback estimates having biases uncorrelated with those impacting climate models. Carbon dioxide concentrations may need to fall below current levels to maintain only a 10% chance of exceeding official 2°C limits on global average temperature change.

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18

Oluwafunmilola, OLUBIYI, Adenike, OLAJIDE, Oluwamayowa Opeyimika, and OLAYEMI Michael Sunday. "A New Approach of Presenting Lindley Expontiated Gumbel Distribution with Application to Environmental Data." International Journal of Membrane Science and Technology 10, no. 2 (October 29, 2023): 2649–57. http://dx.doi.org/10.15379/ijmst.v10i2.2935.

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The Lindley exponentiated Gumbel (LEGu) Distribution, a new family of probability distribution developed for modelling environmental data is introduced in this research paper. The investigation defines the new distribution's basic statistical properties, such as its shape, density function, hazard rate function, moment generation function, and maximum likelihood estimates of its model parameters. The study shows that, in comparison to other baseline distributions and comparators, increasing the number of parameters in the distribution improves its robustness and adaptability, making it more flexible in accommodating different types of data. The model is now more adaptable and can handle a wider range of data sets, making it a useful and effective tool for environmental modelling. The creation of the Lindley exponentiated Gumbel Distribution and the statistical qualities that go along with it bring up new possibilities for the analysis of environmental data, making a significant contribution to the larger initiatives in climate research and decision-making. The results of this study have the potential to advance our comprehension of environmental mechanisms and raise the precision of climate assessments and projections.

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19

Polosin, Vitaly. "Mapping of Beta Distribution for the Study of Dispersed Materials." Materials Science Forum 1049 (January 11, 2022): 295–304. http://dx.doi.org/10.4028/www.scientific.net/msf.1049.295.

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In the study of polydisperse materials, most of the experimental particle size distributions were obtained on bounded intervals. In these cases, it is also desirable to use bounded models with different shapes to simulate the results of studying polydisperse and powder materials. The beta distribution is often used to approximate results due to the fact that this distribution contains many forms for displaying realizations on a limited interval. With the development of computer technology, there has been an increased interest in the use of beta distribution in the modern practice of analyzing results. Meanwhile, there remains a limitation in the use of the beta distribution that is associated with the choice of distribution shape. The possibilities of using known shape measures for mapping beta distribution in this paper is discusses. On the example of the space of shape measure of kurtosis and skewness, the limited use of only probabilistic measures of shapes is illustrated. It is proposed to use the entropy coefficients as an additional informational parameter of the beta distribution shape. On the base of a features comparison of the entropy coefficients for biased and unbiased beta distributions, recommendations for their application are given. By using the example of beta distributions mapping in the space of asymmetry and the entropy coefficient, it is shown that the synergistic combination of probabilistic and informational measures of the shape allows expanding the possibilities of estimating the shape parameters beta distributions. Two methods to display the positions of realizations of beta distributions is proposed. There are trajectories on a constant ratio of shape and realizations position curve on equal values of one parameter. In particular, the features of the choice of beta distributions with negative skewness are discussed.

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20

Ha, Minkyu, Seokgu Gang, Chaewoon Jang, Hyung-Koo Yoon, Jae-Eun Ryou, and Jongwon Jung. "Evaluation of Liquefaction Possibility of Ground Based on Grain Size Distribution and Soil Plasticity." Journal of the Korean Society of Hazard Mitigation 23, no. 1 (February 28, 2023): 191–98. http://dx.doi.org/10.9798/kosham.2023.23.1.191.

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Interest in liquefaction has increased owing to the increasing occurrence of liquefaction in the country. According to previous studies, factors that influence liquefaction include the grain size distribution, plasticity, relative density, overconsolidation ratio, and confining conditions. In this study, the liquefaction possibility was evaluated based on grain size distribution and soil plasticity. Based on the grain size distribution, a clear correlation between the liquefaction resistance of the two samples could not be identified because both samples showed similar grain size distributions. In contrast, in terms of soil plasticity, the liquefaction resistance value increased with increasing plasticity index value. These results indicate that soil plasticity has a significant effect at a similar grain size distribution.

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21

Guo, Zhaozhuang, Shengnan Tian, and Yankui Liu. "A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/2159281.

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In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities.

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22

Lotov, Vladimir Ivanovich. "Exact formulas in some boundary crossing problems for integer-valued random walks." Izvestiya: Mathematics 87, no. 1 (2023): 45–60. http://dx.doi.org/10.4213/im9323e.

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For a wide class of integer-valued random walks, we obtain exact expressions for the distribution of the first excess over level and the corresponding renewal function as well as for the distribution of the trajectory supremum if it is finite. We discuss possibilities of obtaining explicit expressions for pre-stationary and stationary distributions of a random walk with switchings at the strip boundaries. The research is based on the factorization representations for the double moment generating functions of the distributions under study.

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23

Tomy, Lishamol, and Gokul Satish. "A review study on trigonometric transformations of statistical distributions." Biometrics & Biostatistics International Journal 10, no. 4 (October 13, 2021): 130–36. http://dx.doi.org/10.15406/bbij.2021.10.00339.

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For the past few years, various forms of statistical distributions based on trigonometrical transformation were proposed by researchers to model data and thereby finding the suitable distribution to predict the possibilities, and application of it in real life. This article aims to review the recent developments and contributions brought about by the various families of trigonometric functions in statistical distribution and its application in data modelling. Several generalised trigonometric distributions are reviewed and compared along with their properties and uses.

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24

Chen, Bo, and Yuan Li. "Possibility Distribution of Wind Power Fluctuation." International Journal of u- and e-Service, Science and Technology 8, no. 1 (January 31, 2015): 105–16. http://dx.doi.org/10.14257/ijunesst.2015.8.1.10.

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25

Leou, Rong‐Ceng, and Chan‐Nan Lu. "Possibility analysis of distribution system states." Journal of the Chinese Institute of Engineers 19, no. 4 (June 1996): 489–97. http://dx.doi.org/10.1080/02533839.1996.9677812.

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26

YAMADA, Koichi, and Mitsuhiro HONDA. "A Diagnostic Method Using Conditional Possibility Distributions." Journal of Japan Society for Fuzzy Theory and Systems 8, no. 3 (1996): 567–75. http://dx.doi.org/10.3156/jfuzzy.8.3_567.

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27

Ralescu, Dan, and Anca Ralescu. "Characterization of a Class of Possibility Distributions." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23, Suppl. 1 (December 2015): 91–94. http://dx.doi.org/10.1142/s0218488515400073.

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28

TANAKA, Hideo, and Hisao ISHIBUCHI. "Evidence Theory Based on Normal Possibility Distributions." Transactions of the Institute of Systems, Control and Information Engineers 5, no. 6 (1992): 235–43. http://dx.doi.org/10.5687/iscie.5.235.

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29

Hose, Dominik, and Michael Hanss. "On data-based estimation of possibility distributions." Fuzzy Sets and Systems 399 (November 2020): 77–94. http://dx.doi.org/10.1016/j.fss.2020.03.017.

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30

Yager, Ronald R., and Naif Alajlan. "Maxitive Belief Structures and Imprecise Possibility Distributions." IEEE Transactions on Fuzzy Systems 25, no. 4 (August 2017): 768–74. http://dx.doi.org/10.1109/tfuzz.2016.2574930.

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31

BENGUIGUI, LUCIEN, and EFRAT BLUMENFELD-LIEBERTHAL. "FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS." International Journal of Modern Physics C 17, no. 10 (October 2006): 1429–36. http://dx.doi.org/10.1142/s0129183106009953.

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We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

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32

Giakoumakis, Stylianos, and Basil Papadopoulos. "Novel transformation of unimodal (a)symmetric possibility distributions into probability distributions." Fuzzy Sets and Systems 476 (January 2024): 108790. http://dx.doi.org/10.1016/j.fss.2023.108790.

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33

Sauerbrei, Sonja, Uwe Sydow, and Peter J. Plath. "On the Characterization of Foam Decay with Diagram Lattices and Majorization." Zeitschrift für Naturforschung A 61, no. 3-4 (April 1, 2006): 153–65. http://dx.doi.org/10.1515/zna-2006-3-408.

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We present possibilities of comparing and characterizing bubble size distributions during foam decay. We know that the temporal development of bubble size distributions does not follow an ordinary diffusion process. Instead of an equal distribution, we obtain a multi-modal distribution at the end of the rearrangement phase. It turns out that bubble size distributions are comparable to partition diagrams generating Ruch lattices which are expandable by permutations leading to partially ordered sets. If we map the partition diagrams and the bubble size distributions on the Shannon entropy, we obtain similar functions. Furthermore, the set of partition diagrams of a Ruch lattice and the set of the bubble size distributions of foam decay are both partially ordered. Via the theorems of Muirhead and of Hardy, Littlewood and Pólya (classical majorization) we construct transitions between every partition diagram of a Ruch lattice and between every bubble size distribution. These transitions can be reversible or irreversible

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34

Yalaletdinova, A. V., M. A. Malkova, L. V. Enikeеva, and E. A. Kantor. "On the possibility of using the empirical distribution function to quantify the probability of exceeding the water color standards." Theoretical and Applied Ecology, no. 4 (December 23, 2024): 73–82. https://doi.org/10.25750/1995-4301-2024-4-073-082.

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We found that the nature of the distribution of water color values within a year depends on seasonality. Therefore, to take into account the above, further analysis of the distribution of the indicator was carried out for each month. The analysis of water color distributions for January, May, July and October is given as an example. Variation series were plotted and empirical water color distribution functions were calculated for each month. It is revealed that the laws of water color distribution do not correspond to normal and log-normal distributions, but are approximated quite accurately by polynomials (theoretical distribution function). For the obtained polynomials, the domains of definition of the values of the argument x, at which they have all the properties of the distribution function (continuously increase on the interval [0; 1]) are revealed. The hypotheses about the laws of water color distribution tested using Kolmogorov–Smirnov test were confirmed. The methodology used and the resulting water color distribution functions made it possible to calculate the probabilities of an indicator exceeding the specified values, for example, exceeding the standard (20 degrees) for all months. Thus, in January, the probability of not exceeding the standard will is 0.792, in July – 0.562, in October – 0.809, while in May the probability of not exceeding the water color standard is 0.091. Knowledge of the law of water color distribution, taking into account the seasonal characteristics of the studied process, allows to assess the risks of exceeding normative values by the indicator and to use it for making decisions on ensuring normative water quality in terms of color.

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35

Tomanová, Dagmar, and Petr Schneider. "Possibilities of determining the polymodal pore-size distribution from physical adsorption of nitrogen." Collection of Czechoslovak Chemical Communications 52, no. 5 (1987): 1160–66. http://dx.doi.org/10.1135/cccc19871160.

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It is shown, on the basis of experimentally determined adsorption isotherms of physical adsorption of nitrogen on two- and three-component mixtures of fine grained porous glasses with narrow pore-size distributions, that the polymodal mesopore-size distribution curves can be evaluated in case that the porous sample contains groups of mesopores differing rather significantly in size. The differentiation of groups of pores gets worse with wider pores where the demands on the accuracy of the relative pressure measurement grow stronger.

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36

Rumyantseva, Olga D., Andrey S. Shurup, and Dmitriy I. Zotov. "Possibilities for separation of scalar and vector characteristics of acoustic scatterer in tomographic polychromatic regime." Journal of Inverse and Ill-posed Problems 29, no. 3 (January 16, 2021): 407–20. http://dx.doi.org/10.1515/jiip-2020-0141.

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Abstract The inverse wave problem of tomographic type is considered. It consists in reconstruction of several scatterer’s characteristics in the form of spatial distributions for sound speed, medium density, absorption coefficient and power index of its frequency dependence, as well as vector of flow velocity. In the form of a survey material (based on several publications), a sequence of steps is discussed that leads to reconstruction of each individual spatial distribution in the presence of different combinations of the mentioned characteristics. The minimum number of frequencies required for reconstruction is discussed when the complete set of scattering data is available at each of the frequencies. For the first time, two possible approaches to reconstruct the scatterer characteristics in the presence of inhomogeneous spatial distributions of the density and the flow velocity vector are compared, and attention is drawn to the perspectives of reconstruction by functional algorithms in this case. The possibility of separating the sought spatial distributions during the inverse problem solution is illustrated by numerical modeling.

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37

Söderström, S. "Possibilities and limitations of non-homogeneous dose distributions." European Journal of Cancer 29 (January 1993): S28. http://dx.doi.org/10.1016/0959-8049(93)90746-3.

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38

Zakhozhay, O. V. "On the Possibility to Identify a Companion in a Protoplanetary Disk." Proceedings of the International Astronomical Union 10, S314 (November 2015): 211–12. http://dx.doi.org/10.1017/s1743921315005980.

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AbstractIn this paper, I investigate a possibility to detect a brown dwarf companion in a protoplanetary disk based on spectral energy distribution (SED) profile analysis. I present synthetic spectral energy distributions of protoplanetary disks with and without an embedded companion that clears a gap. The computations are performed for a star (0.8 M⊙) and a substellar companion (30 MJ) at an age of 5 Myr embedded in a protoplanetary disk, located at a distance 100 pc from the Sun. Analysis of the SED profile shape indicates that the maximum difference between the fluxes of the systems with and without the companion is ≈ 0.43 Jy at 34 μm.

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39

Masson, Marie-Hélène, and Thierry Denœux. "Inferring a possibility distribution from empirical data." Fuzzy Sets and Systems 157, no. 3 (February 2006): 319–40. http://dx.doi.org/10.1016/j.fss.2005.07.007.

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40

Yager, Ronald R. "On the specificity of a possibility distribution." Fuzzy Sets and Systems 50, no. 3 (September 1992): 279–92. http://dx.doi.org/10.1016/0165-0114(92)90226-t.

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41

Oussalah, Mourad, Hichem Maaref, and Claude Barret. "From adaptive to progressive combination of possibility distributions." Fuzzy Sets and Systems 139, no. 3 (November 2003): 559–82. http://dx.doi.org/10.1016/s0165-0114(02)00513-4.

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42

Lapointe, Stéphane, and Bernard Bobée. "Revision of possibility distributions: A Bayesian inference pattern." Fuzzy Sets and Systems 116, no. 2 (December 2000): 119–40. http://dx.doi.org/10.1016/s0165-0114(98)00367-4.

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43

Antonuyk, Olha, and Alexandr Ushenko. "Possibilities of laser polarimetric diagnostics of umbilical blood and capillary maternal blood." Natural & Mathematical Sciences in Medicine and Medical Education 1, no. 1 (December 27, 2024): 22–29. https://doi.org/10.24061/3083-5887.j.nmsmme.2024.1.i.2.

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A comparative analysis of the two types of samples showed differences in values of the statistical moments of the 3rd and 4th orders. In particular, the statistical moment of the 3rd order (asymmetry) is 2.5 times greater and the 4th parameter (kurtosis) is 2.5 times greater for the blood samples of newborns without pathological changes than the similar parameter for the blood samples of newborns with pathological changes. Fractal analysis showed the transformation of the distribution of power spectra from fractal for coordinate distributions of the Muller matrix element for blood samples without pathology to multifractal (fractal dimensions D1=1.66, D2= 2.90 and D3= 0.56) of blood samples with pathology. The diagnostic sensitivity of the statistical moments of the coordinate distributions of the orientation-phase elements of the Muller p34 matrix of higher orders (3rd and 4th) to structural changes occurring in blood samples of mothers of newborns with a normal physiological state and with pathological changes was revealed. In particular, with pathological changes, the statistical moments of the third order (asymmetry) decrease by 3.5 times, and accordingly, the statistical moment of the fourth order (kurtosis) increases by 2.5 times. The spread of the values of the statistical moments within the two groups did not exceed 5-10% of corresponding average values. The diagnostic possibilities of statistical and fractal analysis of the coordinate distributions of the elements of the Mueller matrix of blood samples of different physiological states of newborns and their mothers have been demonstrated. Fractal and statistical analysis of the coordinate distributions of the orientational elements of the Mueller matrix p33 are diagnostically sensitive when examining the blood of newborns. For maternal blood samples, the statistical analysis of the orientational-phase elements of the Muller p34 matrix (increase in the statistical moments of the 3rd and 4th orders with pathological changes) is diagnostically sensitive.

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44

Kollo, Tõnu, Meelis Käärik, and Anne Selart. "Multivariate Skew t-Distribution: Asymptotics for Parameter Estimators and Extension to Skew t-Copula." Symmetry 13, no. 6 (June 11, 2021): 1059. http://dx.doi.org/10.3390/sym13061059.

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Symmetric elliptical distributions have been intensively used in data modeling and robustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector μ is the location parameter, Σ:p×p is the positive definite scale parameter, p-vector α is the skewness or shape parameter, and the number of degrees of freedom ν is fixed. Special attention is paid to the two-parameter distribution when μ=0 that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of Σ and α. Convergence to the asymptotic distributions is examined in simulation experiments.

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Astola, Jaakko, and Eduard Danielian. "Dediscretization of distributions arising in macroevolution models." Facta universitatis - series: Electronics and Energetics 20, no. 2 (2007): 119–46. http://dx.doi.org/10.2298/fuee0702119a.

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The standard birth-death process with intensities of moderate growth generates stationary skewed distributions suitable for modeling frequency distributions of events arising in large-scale biomolecular systems. We study a large class of such distributions that can be used to model, for instance frequency distributions of the number of expressed genes in the transcriptome, the number of protein domain occurrences in the proteomes etc. In the present paper a new dediscretization approach is suggested discussed and applied to the chosen class. This approach conserves the qualitative properties of the original class of distributions. The advantages of the approach consist in following: 1. It simplifies the form of distributions; 2. It allows simple mathematical analysis of the properties of the original class by applying the tools mathematical analysis continuous functions 3. It allows to find out the optimal form of stationary distributions, i.e. suggests new classes of distributions for biomolecular applications. The deviations of the dediscretized continuous distribution functions from the original distribution functions is estimated. Several typical examples are considered which illustrate the possibilities of the dediscretization approach. The reverse procedure to dediscretization, i.e. the procedure of discretization, back to discrete distributions is described.

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Arratia, Richard, A. D. Barbour, and Simon Tavaré. "On random polynomials over finite fields." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 2 (September 1993): 347–68. http://dx.doi.org/10.1017/s0305004100071620.

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AbstractWe consider random monic polynomials of degree n over a finite field of q elements, chosen with all qn possibilities equally likely, factored into monic irreducible factors. More generally, relaxing the restriction that q be a prime power, we consider that multiset construction in which the total number of possibilities of weight n is qn. We establish various approximations for the joint distribution of factors, by giving upper bounds on the total variation distance to simpler discrete distributions. For example, the counts for particular factors are approximately independent and geometrically distributed, and the counts for all factors of sizes 1, 2, …, b, where b = O(n/log n), are approximated by independent negative binomial random variables. As another example, the joint distribution of the large factors is close to the joint distribution of the large cycles in a random permutation. We show how these discrete approximations imply a Brownian motion functional central limit theorem and a Poisson-Dirichiet limit theorem, together with appropriate error estimates. We also give Poisson approximations, with error bounds, for the distribution of the total number of factors.

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Moshchenko, I., O. Nikitenko, and Yu V. Kozlov. "Possibility of using CMS Maple to study laws of distribution of random variables." Radiotekhnika, no. 204 (April 9, 2021): 128–34. http://dx.doi.org/10.30837/rt.2021.1.204.15.

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The use of CMS Maple for students' practical and independent work is described. The study of random variable distribution laws is actual. Statistical calculations without computer are difficult and require many functional and quintiles tables of standard distributions. This does not contribute to feeling the element of novelty in the material being studied, to be able to arbitrarily change the conditions of tasks, etc., it takes a lot of time in solving applied production problems, which is inappropriate Thus to determine and research random variable distribution laws both in practical applications and in studying we must use special mathematical packages. The most extended of them are Mathcad, MatLab, Mathematica, Maple. Specialized statistical packages (SAS, SPSS, STATISTIKA, STATGRAPHICS) are not relevant to study. Their use for studying requires very high education level in mathematical statistics. Most of the existing math packages allow users to operate at random variables, including the Computer Mathematics System (CMS) Maple. Thus, the purpose of this article is a description of the studying possibilities of the random variables distribution laws with CMS Maple and the application of the acquired skills to the independent work of students. The Maple Statistics Library has a large set of commands for analyzing data, computing various numerical characteristics of random variables, graphing their distribution laws, and for statistical data processing. Thanks to a powerful set of statistical tools, the possibility of symbolic calculations and data processing of CMS Maple, wide possibilities of graphical interpretation of the results obtained not only in a static but also in a dynamic form, it is advisable to use it when studying the topic "Distribution Laws of Random Variables" in students' practical and independent work to use their acquired skills in solving applied problems of science and technology.

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Mathew, Jismi, and Christophe Chesneau. "Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications." Mathematical and Computational Applications 25, no. 4 (October 1, 2020): 65. http://dx.doi.org/10.3390/mca25040065.

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It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.

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MYRONYUK, MARGARYTA. "HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS." Journal of the Australian Mathematical Society 88, no. 1 (January 22, 2010): 93–102. http://dx.doi.org/10.1017/s1446788709000378.

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AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

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E. Gaume. "On the asymptotic behavior of flood peak distributions – theoretical results." Hydrology and Earth System Sciences Discussions 2, no. 5 (September 1, 2005): 1835–64. http://dx.doi.org/10.5194/hessd-2-1835-2005.

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Abstract. This paper presents some analytical results and numerical illustrations on the asymptotic properties of flood peak distributions obtained through derived flood frequency approaches. It confirms and extends the results of previous works: i.e. the shape of the flood peak distributions are asymptotically controlled by the rainfall statistical properties, given limited and reasonable assumptions concerning the rainfall-runoff process. This previous result is partial so far: only two types of rainfall intensity distributions have been considered (extreme value distributions of types I and II), and the impact of the rainfall spatial heterogeneity has not been studied. From a practical point of view, it provides a general framework for analysis of the outcomes of previous works based on derived flood frequency approaches and leads to some proposals for the estimation of very large return-period flood quantiles. This paper, focussed on asymptotic distribution properties, does not propose any new approach for the extrapolation of flood frequency distribution to estimate intermediate return period flood quantiles. Nevertheless, the large distance between frequent flood peak values and the asymptotic values as well as the simulations conducted in this paper help quantifying the ill condition of the problem of flood frequency distribution extrapolation: it illustrates how large the range of possibilities for the shapes of flood peak distributions is.

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