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For every continuous random variable with probability density function (pdf) f(x) a corresponding dual pdf f~* (x) can be defined in terms of the moment generating function (mgf) or the characteristic function (cf). In this note,...
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For every continuous random variable with probability density function (pdf) f(x) a corresponding dual pdf f~* (x) can be defined in terms of the moment generating function (mgf) or the characteristic function (cf). In this note, formulas for f~*(x) are provided for the most applied continuous distributions (27 of them). More than ten motivating applications are described. The results give rise to many new distributions that are not known in the current literature.
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In the present work a new version of the Probabilistic Transformation Method (PTM) has been reported for the study of linear systems subjected to static random loads. Even if this application could appear trivial, it allows to fin...
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In the present work a new version of the Probabilistic Transformation Method (PTM) has been reported for the study of linear systems subjected to static random loads. Even if this application could appear trivial, it allows to find some exact results, difficulty obtainable by other approaches. In particular, some interesting results have been obtained in the case of uniformly distributed random loads. For a generic vector of random loads this version of the PTM has allowed to obtain the characteristic function (cf) of any response elements in a very simple and effective way.
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There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probabili...
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There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDFs for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.
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In this paper we will consider the system for noncoherent demodulation of BFSK signal in the presence of Gaussian noise. We will derive the probability density function of BFSK receiver output signal and the joint probability dens...
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In this paper we will consider the system for noncoherent demodulation of BFSK signal in the presence of Gaussian noise. We will derive the probability density function of BFSK receiver output signal and the joint probability density function of the output signal and its derivative in order to view the influence of the Gaussian noise and fading on the performances of the BFSK system.
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Las estrellas Cefeidas han sido de gran relevancia para la determinación de distancias tanto en la Galaxia como a escala cosmológica. Debido a que, hasta el momento, la mayor parte de las Cefeidas cercanas observadas se encuentr...
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Las estrellas Cefeidas han sido de gran relevancia para la determinación de distancias tanto en la Galaxia como a escala cosmológica. Debido a que, hasta el momento, la mayor parte de las Cefeidas cercanas observadas se encuentran en la vecindad solar, se juzga pertinente un estudio probabilístico sobre su distribución, no solo en la vecindad solar sino también en toda la Vía Láctea, pues deben estar jugando un papel importante para mantener la estructura de nuestra Galaxia. Partiendo de 187 Cefeidas observadas en la Vía Láctea, se presenta una función de densidad de probabilidad normal que sirvió para elaborar un modelo en tres dimensiones que permite encontrar la zona de más alta concentración de Cefeidas y de paso, con ella, predecir la existencia de Cefeidas en zonas ceranas a toda la Galaxia. Asmismo, se da a conocer una segunda distribución de probabilidad, normal también, pero en la vecindad del eje galáctico, a fin de elaborar otro modelo que permita predecir la existencia de estrellas Cefeidas dentro de la Vía Láctea y en la vecindad del sol.ABSTRACTThe Cepheid stars have been very relevant for the determination ofdistances both in the Galaxy and also at cosmological scale. Because, so far, most of the nearby observed Cepheids are in the solar neighborhood, a probabilistic study about their distribution in the solar neighborhood and in the whole Milky Way is pertinent, since they must be playing an important role for keeping the structure of our Galaxy. Starting from the in the Milky Way already 187 observed Cepheids, a normal probability density function for their distribution in the Galaxy is presented, which is used to carry out a model which allows to find the high concentration zone of Cepheids and, in turn, with it, to predict the existence of Cepheids in the neighborhood of the Galaxy. A second model has been done, in order to prognosticate the existence of Cepheids within the milky way and in the neigborhood of the sun.
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Z. Chair and P.R. Varshney (1986) solved the data fusion problem for fixed binary local detectors with statistically independent decisions. Their solution is generalized by using the Bahadur-Lazarsfeld expansion of probability den...
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Z. Chair and P.R. Varshney (1986) solved the data fusion problem for fixed binary local detectors with statistically independent decisions. Their solution is generalized by using the Bahadur-Lazarsfeld expansion of probability density functions. The optimal data fusion rule is developed for correlation local binary decisions, in terms of the conditional correlation coefficients of all orders. It is shown that when all these coefficients are zero, the rule coincides with the original Chair-Varshney design.
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Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of dist...
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Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of distances from a given point, a probability distribution mapping function is introduced here. The approximation of this function in a form of a suitable power of the distance is presented. How to state this power-the distribution mapping exponent-is described. This exponent is used for probability density estimation in high-dimensional spaces and for classification. A close relation of the exponent to a singularity exponent is discussed. It is also shown that this classifier exhibits better behavior (classification accuracy) than other kinds of classifiers for some tasks.
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摘要 :
Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of dist...
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Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of distances from a given point, a probability distribution mapping function is introduced here. The approximation of this function in a form of a suitable power of the distance is presented. How to state this power—the distribution mapping exponent—is described. This exponent is used for probability density estimation in high-dimensional spaces and for classification. A close relation of the exponent to a singularity exponent is discussed. It is also shown that this classifier exhibits better behavior (classification accuracy) than other kinds of classifiers for some tasks.
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Recently the proportional reversed hazard model has received a considerable amount of attention in the statistical literature. The main aim of this paper is to introduce a bivariate proportional reversed hazard model and discuss i...
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Recently the proportional reversed hazard model has received a considerable amount of attention in the statistical literature. The main aim of this paper is to introduce a bivariate proportional reversed hazard model and discuss its different properties. In most of the cases the joint probability distribution function can be expressed in compact forms. The maximum likelihood estimators cannot be expressed in explicit forms in most of the cases. EM algorithm has been proposed to compute the maximum likelihood estimators of the unknown parameters. For illustrative purposes two data sets have been analyzed and the performances are quite satisfactory.
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In this letter, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advant...
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In this letter, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of this class is that the requirements could be readily verified for a given distribution.
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