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A new family of generalized distributions

CORDEIRO, Gauss M.; CASTRO, Mario de
Fonte: TAYLOR & FRANCIS LTD Publicador: TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.18%
Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.; CNPq, Brazil; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Distribuição de probabilidade e dimensionamento amostral para tamanho de partícula em gramíneas forrageiras; Probability distribution and sample dimension for particle size in forage grasses

Navarette López, Claudia Fernanda
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 16/01/2009 PT
Relevância na Pesquisa
46.18%
O objetivo deste trabalho foi identificar a distribuição de probabilidade da variável tamanho de partícula em gramíneas forrageiras e fazer um dimensionamento amostral. Para isto foi realizada uma analise exploratória dos dados obtidos de um experimento planejado em blocos casualizados, a cada sub-amostra do conjunto de dados foram ajustadas as distribuições normal, gama, beta e Weibull. Foram realizados os testes de aderência não paramétricos de Kolmogorov-Smirnov, Lilliefos, Cramer-von Mises e Anderson-Darling para avaliar o ajuste as distribuições. A estimativa do valor do logaritmo da função de máxima verossimilhança e indicativo da distribuição que melhor descreveu o conjunto de dados, assim como os critérios de informação de Akaike (AIC) e de informação bayesiano (BIC). Foram feitas simulações a partir dos parâmetros obtidos e feitos os testes não paramétricos para avaliar o ajuste com diferentes tamanhos de amostras. Encontrou-se que os dados n~ao seguem a distribuição normal, pois há assimetria nos histogramas melhor descritos pelas distribuições beta e Weibull. Os testes mostraram que as distribuições gama, beta e Weibull ajustam-se melhor aos dados porem pelo maior valor do logaritmo da função de verossimilhança...

As distribuições Kumaraswamy-log-logística e Kumaraswamy-logística; Distributions Kumaraswamy-log-logistic and Kumaraswamy-logistic

Santana, Tiago Viana Flor de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 18/10/2010 PT
Relevância na Pesquisa
46.17%
Neste trabalho apresenta-se duas novas distribuições de probabilidade obtidas de dois métodos de generalização da distribuição log-logística com dois parâmetros (LL(?,?)). O primeiro método descrito em Marshall e Olkin (1997) transforma a nova distribuição, agora com três parâmetros e denominada distribuição log-logística modificada (LLM (v,?,?)), mais flexível porém, não muda a forma geral da função de taxa de falha e o novo parâmetro v, não influência no cálculo da assimetria e curtose. O segundo método utiliza a classe de distribuições Kumaraswamy proposta por Cordeiro e Castro (2010), para construir a nova distribuição de probabilidade, denominada distribuição Kumaraswamy log-logística (Kw-LL(a,b,?,?)), a qual considera dois novos parâmetros a e b obtendo ganho nas formas da função de taxa de falha, que agora além de modelar dados onde a função de taxa de falha tem forma decrescente e unimodal, modela forma crescente e forma de U. Também foi proposto as distribuições logística modificada (LM (v,µ,?)) e Kumaraswamy logística (Kw-L (a,b, µ,?)$) para a variável Y=log(T), em que T ~ LLM (v,?,?) no caso da distribuição logística modificada e T ~ Kw-LL(a,b,?,?) no caso da distribuição Kw-L. Com reparametrização ? = exp(µ) e ? = 1/?. Da mesma forma que a distribuição LLM...

Modelo de regressão gama-G em análise de sobrevivência ; Gama-G regression model in survival analysis

Hashimoto, Elizabeth Mie
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 15/03/2013 PT
Relevância na Pesquisa
36.16%
Dados de tempo de falha são caracterizados pela presença de censuras, que são observações que não foram acompanhadas até a ocorrência de um evento de interesse. Para estudar o comportamento de dados com essa natureza, distribuições de probabilidade são utilizadas. Além disso, é comum se ter uma ou mais variáveis explicativas associadas aos tempos de falha. Dessa forma, o objetivo geral do presente trabalho é propor duas novas distribuições utilizando a função geradora de distribuições gama, no contexto de modelos de regressão em análise de sobrevivência. Essa função possui um parâmetro de forma que permite criar famílias paramétricas de distribuições que sejam flexíveis para capturar uma ampla variedade de comportamentos simétricos e assimétricos. Assim, a distribuição Weibull e a distribuição log-logística foram modificadas, dando origem a duas novas distribuições de probabilidade, denominadas de gama-Weibull e gama-log-logística, respectivamente. Consequentemente, os modelos de regressão locação-escala, de longa-duração e com efeito aleatório foram estudados, considerando as novas distribuições de probabilidade. Para cada um dos modelos propostos, foi utilizado o método da máxima verossimilhança para estimar os parâmetros e algumas medidas de diagnóstico de influência global e local foram calculadas para encontrar possíveis pontos influentes. No entanto...

Distribuições das classes Kumaraswamy generalizada e exponenciada: propriedades e aplicações; Distributions of the generalized Kumaraswamy and exponentiated classes: properties and applications

Braga Junior, Antonio Carlos Ricardo
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 04/04/2013 PT
Relevância na Pesquisa
45.92%
Recentemente, Cordeiro e de Castro (2011) apresentaram uma classe generalizada baseada na distribuição Kumaraswamy (Kw-G). Essa classe de distribuições modela as formas de risco crescente, decrescente, unimodal e forma de U ou de banheira. Uma importante distribuição pertencente a essa classe é a distribuição Kumaraswamy Weibull modificada (KwMW) proposta por Cordeiro; Ortega e Silva (2013). Com isso foi utilizada essa distribuição para o desenvolvimento de algumas novas propriedades e análise bayesiana. Além disso, foi desenvolvida uma nova distribuição de probabilidade a partir da distribuição gama generalizada geométrica (GGG) que foi denominada de gama generalizada geométrica exponenciada (GGGE). Para a nova distribuição GGGE foram calculados os momentos, a função geradora de momentos, os desvios médios, a confiabilidade e as estatísticas de ordem. Desenvolveu-se o modelo de regressão log-gama generalizada geométrica exponenciada. Para a estimação dos parâmetros, foram utilizados os métodos de máxima verossimilhança e bayesiano e, finalmente, para ilustrar a aplicação da nova distribuição foi analisado um conjunto de dados reais.; Recently, Cordeiro and de Castro (2011) showed a generalized class based on the Kumaraswamy distribution (Kw-G). This class of models has crescent risk forms...

Contribuições teoricas para o estudo de funções de distribuição correlacionadas em um canal sem fio; Theoretical contributions to the study of correlated distributions funcions of wireless channels

Rausley Adriano Amaral de Souza
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 21/05/2009 PT
Relevância na Pesquisa
36.2%
Em comunicações móveis, o desvanecimento por múltiplos percursos é modelado por várias distribuições incluindo Hoyt, Rayleigh, Weibull, Nakagami-m e Rice. Nesta tese, são deduzidas expressões exatas para o modelo de duas variáveis Hoyt (Nakagami-q) com correlação arbitrária em um ambiente não estacionário. De forma específica, as seguintes estatísticas são encontradas: função densidade de probabilidade conjunta, função de distribuição cumulativa conjunta, coeficiente de correlação e algumas estatísticas relacionadas ao parâmetro SNR na saída do combinador de seleção, a saber, probabilidade de indisponibilidade e função densidade de probabilidade. As expressões fazem uso dos polinômios de Laguerre generalizados. Elas são matematicamente tratáveis e possuem flexibilidade suficiente para acomodar um grande número de cenários de correlação, úteis na análise de um ambiente com desvanecimento mais geral. Depois disto, aproveitando os resultados previamente deduzidos, expressões exatas relacionadas a processos Nakagami-m com duas variáveis com correlação arbitrária e parâmetros de desvanecimento igualmente arbitrários são encontradas. De forma mais específica, as seguintes estatísticas são obtidas neste trabalho: função geratriz de momentos...

Probabilistic distributions of regional climate change and their application in risk analysis of wheat production

Luo, Q.; Jones, R.; Williams, M.; Bryan, B.; Bellotti, W.
Fonte: Inter-Research Publicador: Inter-Research
Tipo: Artigo de Revista Científica
Publicado em //2005 EN
Relevância na Pesquisa
36.15%
Downscaled outputs from 9 climate models and information from the 2000 Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) were used to construct probability distributions of regional climate change for Roseworthy, South Australia. The construction of probability distribution for regional climate change involved the identification, quantification and treatment of uncertainties from greenhouse gas (GHG) emission scenarios, climate sensitivity and local climate change. Monte Carlo random sampling techniques were applied to component ranges of uncertainty defined by quantified upper and lower limits, assuming uniform probability over each range. Construction of resulting probability distributions of regional climate provided a framework for risk analysis. These probabilities were applied to the Agricultural Production System sIMulator (APSIM)-Wheat model to evaluate potential wheat production at Roseworthy for the year 2080 through the identification of critical yield thresholds. The conditional probability of not meeting the critical yield threshold increased from 27% under baseline conditions to 45% under the median probability for the year 2080, indicating less profitable wheat production in the study area.; Qunying Luo...

Dispersion measure for symmetric, stable probability distributions

Tyhtila, Jussi I.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.14%
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton invariant under addition, up to a scale. Noteworthly they have power-law type of decay and therefore they are an excellent model for modelling many natural phenomena, such as earthquakes, financial returns, and a multitude of social phenomena such as size distributions of cities and firms \cite{scaling}. The major problem concerning them is that they have an infinite variance \cite{GK} and therefore their practical applicability is somewhat limited. Also they generally do not possess a density expressible in an analytic form. This study proposes a dispersion measure for them, drawing ideas from Fisher information, differential geometry and most importantly, the uncertainty principle for Fourier transform pairs \cite{Weyl}. The study begins with a brief discussion on characteristic functions and their relation to Fourier transforms and their properties, proceeds to a brief presentation of stable distributions and accumulates in defining a concept of \textit{characteristic curvature}, which is proposed as a suitable measure of dispersion for class of stable distributions. Characteristic curvature satisfies the familiar scaling property for stable processes...

Conflations of Probability Distributions

Hill, Theodore P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.24%
The conflation of a finite number of probability distributions P_1,..., P_n is a consolidation of those distributions into a single probability distribution Q=Q(P_1,..., P_n), where intuitively Q is the conditional distribution of independent random variables X_1,..., X_n with distributions P_1,..., P_n, respectively, given that X_1= ... =X_n. Thus, in large classes of distributions the conflation is the distribution determined by the normalized product of the probability density or probability mass functions. Q is shown to be the unique probability distribution that minimizes the loss of Shannon Information in consolidating the combined information from P_1,..., P_n into a single distribution Q, and also to be the optimal consolidation of the distributions with respect to two minimax likelihood-ratio criteria. When P_1,..., P_n are Gaussian, Q is Gaussian with mean the classical weighted-mean-squares reciprocal of variances. A version of the classical convolution theorem holds for conflations of a large class of a.c. measures.; Comment: Additional reference, revised abstract, revised introduction (idempotency), revised title, and revised introduction to section 7; these changes plus converting the manuscript from plain tex to latex shortened the paper to 23 pages

A simple derivation and classification of common probability distributions based on information symmetry and measurement scale

Frank, Steven A.; Smith, Eric
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/10/2010
Relevância na Pesquisa
36.27%
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His approach was phenomenological: a differential equation that generated common distributions without any underlying conceptual basis for why common distributions have particular forms and what explains the familial relations. Pearson's system and its descendants remain the most popular systematic classification of probability distributions. Here, we unify the disparate forms of common distributions into a single system based on two meaningful and justifiable propositions. First, distributions follow maximum entropy subject to constraints, where maximum entropy is equivalent to minimum information. Second, different problems associate magnitude to information in different ways, an association we describe in terms of the relation between information invariance and measurement scale. Our framework relates the different continuous probability distributions through the variations in measurement scale that change each family of maximum entropy distributions into a distinct family.; Comment: 17 pages, 0 figures

Fourier and Cauchy-Stieltjes transforms of power laws including stable distributions

Hasebe, Takahiro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.18%
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers. This class includes stable distributions in probability and also non-commutative probability theories. We also characterize the class in terms of the Cauchy-Stieltjes transform and the Voiculescu transform. If the stability index is greater than one, stable distributions in probability theory do not belong to that class, while they do in non-commutative probability.; Comment: 18 pages, Subsection 2.5 withdrawn, accepted for publication in Internat. J. Math

How to read probability distributions as statements about process

Frank, Steven A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.16%
Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale of information, opportunities arise to understand the processes that generate the commonly observed patterns. Probability expressions may be parsed into four components: the dissipation of all information, except the preservation of average values, taken over the measurement scale that relates changes in observed values to changes in information, and the transformation from the underlying scale on which information dissipates to alternative scales on which probability pattern may be expressed. Information invariances set the commonly observed measurement scales and the relations between them. In particular, a measurement scale for information is defined by its invariance to specific transformations of underlying values into measurable outputs. Essentially all common distributions can be understood within this simple framework of information invariance and measurement scale.; Comment: v2: added table of contents, adjusted section numbers v3: minor editing, updated reference

Improvements of Track Fitting with Well Tuned Probability Distributions for Silicon Strip Detectors

Landi, Gregorio; Landi, Giovanni E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/04/2014
Relevância na Pesquisa
36.24%
The construction of a well tuned probability distributions is illustrated in synthetic way, these probability distributions produce faithful realizations of the impact point distributions for particles in silicon strip detector. Their use for track fitting shows a drastic improvements of a factor two, for the low noise case, and a factor three, for the high noise case, respect to the standard approach. The tracks are well reconstructed even in presence of hits with large errors, with a surprising effect of hit discarding. The applications illustrated are simulations of the PAMELA tracker, but other type of trackers can be handled similarly. The probability distributions are calculated for the center of gravity algorithms, and they are very different from gaussian probabilities. These differences are crucial to accurately reconstruct tracks with high error hits and to produce the effective discarding of the too noisy hits (outliers). The similarity of our distributions with the Cauchy distribution forced us to abandon the standard deviation for our comparisons and instead use the full width at half maximum. A set of mathematical approaches must be developed for these applications, some of them are standard in wide sense, even if very complex. One is essential and...

Multidimensional Shintani zeta functions and zeta distributions on R^d

Aoyama, Takahiro; Nakamura, Takashi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.18%
The class of Riemann zeta distribution is one of the classical classes of probability distributions on R. Multidimensional Shintani zeta function is introduced and its definable probability distributions on R^d are studied. This class contains some fundamental probability distributions such as binomial and Poisson distributions. The relation with multidimensional polynomial Euler product, which induces multidimensional infinitely divisible distributions on R^d, is also studied.; Comment: 15 pages. arXiv admin note: text overlap with arXiv:1204.4041

Quantifying knowledge with a new calculus for belief functions - a generalization of probability theory

Kerkvliet, Timber; Meester, Ronald
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/12/2015
Relevância na Pesquisa
36.16%
We first show that there are practical situations in for instance forensic and gambling settings, in which applying classical probability theory, that is, based on the axioms of Kolmogorov, is problematic. We then introduce and discuss Shafer belief functions. Technically, Shafer belief functions generalize probability distributions. Philosophically, they pertain to individual or shared knowledge of facts, rather than to facts themselves, and therefore can be interpreted as generalizing epistemic probability, that is, probability theory interpreted epistemologically. Belief functions are more flexible and better suited to deal with certain types of uncertainty than classical probability distributions. We develop a new calculus for belief functions which does not use the much criticized Dempster's rule of combination, by generalizing the classical notions of conditioning and independence in a natural and uncontroversial way. Using this calculus, we explain our rejection of Dempster's rule in detail. We apply the new theory to a number of examples, including a gambling example and an example in a forensic setting. We prove a law of large numbers for belief functions and offer a betting interpretation similar to the Dutch Book Theorem for probability distributions.

Joint Probability Distributions for a Class of Non-Markovian Processes

Baule, A.; Friedrich, R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.21%
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.; Comment: 13 pages, 1 figure

Nonadditive Entropies Yield Probability Distributions with Biases not Warranted by the Data

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/12/2013
Relevância na Pesquisa
36.18%
Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics

Dzhafarov, Ehtibar N.; Kujala, Janne V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.16%
Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov's probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice-Bob EPR paradigm, non-contextuality means that the identity of Alice's spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis \alphai chosen by Alice, irrespective of Bob's axis \betaj (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice's and Bob's spins are identified as Aij and Bij, even though their distributions are determined by, respectively, \alphai alone and \betaj alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins Aij,Bij across all values of \alphai,\betaj are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs \left(Aij,Aij'\right) and \left(Bij,Bi'j\right) with \alphai\not=\alphai' and \betaj\not=\betaj' (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of Aij\not=Aij' and Bij\not=Bi'j). Thus, one can achieve a complete KPT characterization bof the Bell-type inequalities...

Random fractals and Probability metrics

Hutchinson, John; Ruschendorf, Ludger
Fonte: Applied Probability Trust Publicador: Applied Probability Trust
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.07%
New metrics are introduced in the space of random measures and are applied, with various modifications of the contraction method, to prove existence and uniqueness results for self-similar random fractal measures. We obtain exponential convergence, both in distribution and almost surely, of an iterative sequence of random measures (defined by means of the scaling operator) to a unique self-similar random measure. The assumptions are quite weak, and correspond to similar conditions in the deterministic case. The fixed mass case is handled in a direct way based on regularity properties of the metrics and the properties of a natural probability space. Proving convergence in the random mass case needs additional tools, such as a specially adapted choice of the space of random measures and of the space of probability distributions on measures, the introduction of reweighted sequences of random measures and a comparison technique.

Expected Utility from Multinomial Second-order Probability Distributions

Sundgren,David
Fonte: Instituto Politécnico Nacional, Centro de Innovación y Desarrollo Tecnológico en Cómputo Publicador: Instituto Politécnico Nacional, Centro de Innovación y Desarrollo Tecnológico en Cómputo
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2010 EN
Relevância na Pesquisa
36.24%
We consider the problem of maximizing expected utility when utilities and probabilities are given by discrete probability distributions so that expected utility is a discrete stochastic variable. As for discrete second-order distributions, that is probability distributions where the variables are themselves probabilities, the multinomial family is a reasonable choice at least if first-order probabilities are interpreted as relative frequencies. We suggest a decision rule that reflects the uncertainty present in distribution-based probabilities and utilities and we show an example of this rule in action with multinomial second-order distributions.