A generalized normal distribution

Nadarajah, Saralees

doi:10.1080/02664760500079464

Cited by 398 publications

(209 citation statements)

References 1 publication

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“…(b) The spatial kernel In this study, we modelled the spatial kernel with a generalized normal distribution [37]. In Lindström et al [17] this was extended to two-dimensional symmetrical kernels.…”

Section: Methodsmentioning

confidence: 99%

The shape of the spatial kernel and its implications for biological invasions in patchy environments

2010

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Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.

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Section: Methodsmentioning

confidence: 99%

The shape of the spatial kernel and its implications for biological invasions in patchy environments

2010

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“…The exponential power distribution, also called the generalized error distribution or generalized normal distribution, on the other hand, can model the error with both positive and negative kurtosis (Box & Tiao, 1973;Nadarajah, 2005). The exponential …”

Section: Exponential Power Distributionmentioning

confidence: 99%

Modeling error distributions of growth curve models through Bayesian methods

Zhang

2015

Behav Res

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Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and nonnormal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

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“…A treatment of some mathematical properties of GND(µ, σ, κ) is provided in Nadarajah (2005). The properties studied there include moments, variance, skewness, kurtosis, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy, the asymptotic distribution of the extreme order statistics, and estimation procedures by the methods of moments and maximum likelihood.…”

Section: Introductionmentioning

confidence: 99%

On the characteristic function of the generalized normal distribution

Pogány

Nadarajah

2009

Comptes Rendus. Mathématique

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For the first time, an explicit closed form expression is derived for the characteristic function of the generalized normal distribution (GND). Also derived is an expression for the correlation coefficient between variate-values and their ranks in samples from the GND. The expression for the former involves the Fox-Wright generalized confluent hypergeometric 1 Ψ 0 -function, while the latter is expressed via the Gaussian hypergeometric 2 F 1 .

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A generalized normal distribution

Cited by 398 publications

References 1 publication

The shape of the spatial kernel and its implications for biological invasions in patchy environments

The shape of the spatial kernel and its implications for biological invasions in patchy environments

Modeling error distributions of growth curve models through Bayesian methods

On the characteristic function of the generalized normal distribution

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