Constructing the frequency and wave normal distribution of whistler-mode wave power

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.

Bimodal extension based on the skew-normal distribution with application to pollen data

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.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

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.

A Generalized Log-Normal Model for Grouped Survival Data

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inferences about the coefficient of correlation in the standard bivariate normal distribution

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.

An extension of the half-normal distribution

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.

Mesenchymal progenitor cell markers in human articular cartilage: normal distribution and changes in osteoarthritis

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.

Reliability studies of the skew normal distribution

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.

The Dynamin-like Protein DLP1 Is Essential for Normal Distribution and Morphology of the Endoplasmic Reticulum and Mitochondria in Mammalian Cells

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.

Tables of factors for one-sided tolerance limits for normal distribution,

Mode of access: Internet.

Size frequency distribution of the β-amyloid (aβ) deposits in dementia with Lewy bodies with associated Alzheimer’s disease pathology

The objective is to study beta-amyloid (Abeta) deposition in dementia with Lewy bodies (DLB) with Alzheimer's disease (AD) pathology (DLB/AD). The size frequency distributions of the Abeta deposits were studied and fitted by log-normal and power-law models. Patients were ten clinically and pathologically diagnosed DLB/AD cases. Size distributions had a single peak and were positively skewed and similar to those described in AD and Down's syndrome. Size distributions had smaller means in DLB/AD than in AD. Log-normal and power-law models were fitted to the size distributions of the classic and diffuse deposits, respectively. Size distributions of Abeta deposits were similar in DLB/AD and AD. Size distributions of the diffuse deposits were fitted by a power-law model suggesting that aggregation/disaggregation of Abeta was the predominant factor, whereas the classic deposits were fitted by a log-normal distribution suggesting that surface diffusion was important in the pathogenesis of the classic deposits.

Do β-amyloid (Aβ) deposits in patients with Alzheimer's disease and Down's syndrome grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and classic β- amyloid (Aβ) deposits were studied in single sections of cortical tissue from patients with Alzheimer's disease (AD) and Down's syndrome (DS) and compared with those predicted by the log-normal model. In a sample of brain regions, these size distributions were compared with those obtained by serial reconstruction through the tissue and the data used to adjust the size distributions obtained in single sections. The adjusted size distributions of the diffuse, primitive and classic deposits deviated significantly from a log-normal model in AD and DS, the greatest deviations from the model being observed in AD. More Aβ deposits were observed close to the mean and fewer in the larger size classes than predicted by the model. Hence, the growth of Aβ deposits in AD and DS does not strictly follow the log-normal model, deposits growing to within a more restricted size range than predicted. However, Aβ deposits grow to a larger size in DS compared with AD which may reflect differences in the mechanism of Aβ formation.

Factors determining the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease

The size frequency distributions of discrete β-amyloid (Aβ) deposits were studied in single sections of the temporal lobe from patients with Alzheimer's disease. The size distributions were unimodal and positively skewed. In 18/25 (72%) tissues examined, a log normal distribution was a good fit to the data. This suggests that the abundances of deposit sizes are distributed randomly on a log scale about a mean value. Three hypotheses were proposed to account for the data: (1) sectioning in a single plane, (2) growth and disappearance of Aβ deposits, and (3) the origin of Aβ deposits from clusters of neuronal cell bodies. Size distributions obtained by serial reconstruction through the tissue were similar to those observed in single sections, which would not support the first hypothesis. The log normal distribution of Aβ deposit size suggests a model in which the rate of growth of a deposit is proportional to its volume. However, mean deposit size and the ratio of large to small deposits were not positively correlated with patient age or disease duration. The frequency distribution of Aβ deposits which were closely associated with 0, 1, 2, 3, or more neuronal cell bodies deviated significantly from a log normal distribution, which would not support the neuronal origin hypothesis. On the basis of the present data, growth and resolution of Aβ deposits would appear to be the most likely explanation for the log normal size distributions.

Income distribution dependence of poverty measure:a theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the 'global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy. © 2006 Elsevier B.V. All rights reserved.

Joint Densities of Correlation Coefficients for Samples from Multivariate Standard Normal Distribution

2000 Mathematics Subject Classification: 62H10.