972 resultados para sinh-normal distribution


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In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

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It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

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Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

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Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

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lecture for COMP6235

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We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

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The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

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This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright (C) 2009 John Wiley & Sons, Ltd.

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Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

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The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

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In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.

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INTRODUCTION: Recent findings suggest that articular cartilage contains mesenchymal progenitor cells. The aim of this study was to examine the distribution of stem cell markers (Notch-1, Stro-1 and VCAM-1) and of molecules that modulate progenitor differentiation (Notch-1 and Sox9) in normal adult human articular cartilage and in osteoarthritis (OA) cartilage. METHODS: Expression of the markers was analyzed by immunohistochemistry (IHC) and flow cytometry. Hoechst 33342 dye was used to identify and sort the cartilage side population (SP). Multilineage differentiation assays including chondrogenesis, osteogenesis and adipogenesis were performed on SP and non-SP (NSP) cells. RESULTS: A surprisingly high number (>45%) of cells were positive for Notch-1, Stro-1 and VCAM-1 throughout normal cartilage. Expression of these markers was higher in the superficial zone (SZ) of normal cartilage as compared to the middle zone (MZ) and deep zone (DZ). Non-fibrillated OA cartilage SZ showed reduced Notch-1 and Sox9 staining frequency, while Notch-1, Stro-1 and VCAM-1 positive cells were increased in the MZ. Most cells in OA clusters were positive for each molecule tested. The frequency of SP cells in cartilage was 0.14 +/- 0.05% and no difference was found between normal and OA. SP cells displayed chondrogenic and osteogenic but not adipogenic differentiation potential. CONCLUSIONS: These results show a surprisingly high number of cells that express putative progenitor cell markers in human cartilage. In contrast, the percentage of SP cells is much lower and within the range of expected stem cell frequency. Thus, markers such as Notch-1, Stro-1 or VCAM-1 may not be useful to identify progenitors in cartilage. Instead, their increased expression in OA cartilage implicates involvement in the abnormal cell activation and differentiation process characteristic of OA.

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It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

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The dynamin family of large GTPases has been implicated in vesicle formation from both the plasma membrane and various intracellular membrane compartments. The dynamin-like protein DLP1, recently identified in mammalian tissues, has been shown to be more closely related to the yeast dynamin proteins Vps1p and Dnm1p (42%) than to the mammalian dynamins (37%). Furthermore, DLP1 has been shown to associate with punctate vesicles that are in intimate contact with microtubules and the endoplasmic reticulum (ER) in mammalian cells. To define the function of DLP1, we have transiently expressed both wild-type and two mutant DLP1 proteins, tagged with green fluorescent protein, in cultured mammalian cells. Point mutations in the GTP-binding domain of DLP1 (K38A and D231N) dramatically changed its intracellular distribution from punctate vesicular structures to either an aggregated or a diffuse pattern. Strikingly, cells expressing DLP1 mutants or microinjected with DLP1 antibodies showed a marked reduction in ER fluorescence and a significant aggregation and tubulation of mitochondria by immunofluorescence microscopy. Consistent with these observations, electron microscopy of DLP1 mutant cells revealed a striking and quantitative change in the distribution and morphology of mitochondria and the ER. These data support very recent studies by other authors implicating DLP1 in the maintenance of mitochondrial morphology in both yeast and mammalian cells. Furthermore, this study provides the first evidence that a dynamin family member participates in the maintenance and distribution of the ER. How DLP1 might participate in the biogenesis of two presumably distinct organelle systems is discussed.

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