Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.     

New class of Johnson distributions and its associated regression model for rates and proportions

By starting from the Johnson distribution pioneered by Johnson ( 1949 ), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathematical properties of the new family is provided. We briefly discuss estimation of the model parameters of the new class of distributions based on two estimation methods. Additionally, a new regression model is introduced by considering the distribution proposed in this article, which is useful for situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. The regression model allows to model both location and dispersion effects. We define two residuals for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence and generalized leverage. Finally, an application to real data is presented to show the usefulness of the new regression model.     

Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions

In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta , Gupta , and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribution. We present two real life data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.     

Circular distributions based on nonnegative trigonometric sums

A new family of distributions for circular random variables is proposed. It is based on nonnegative trigonometric sums and can be used to model data sets which present skewness and/or multimodality. In this family of distributions, the trigonometric moments are easily expressed in terms of the parameters of the distribution. The proposed family is applied to two data sets, one related with the directions taken by ants and the other with the directions taken by turtles, to compare their goodness of fit versus common distributions used in the literature.     

k-长DNA子序列频数分布研究

在详细阐述了生成DNA序列分形图像的Hao方法后,提出一种能够直观显示k-长DNA子序列频数分布差异性的三维频数分布图生成方法。把3D频数分布图转化为1D对数频谱图,突出显示了频数分布的局部特征,提出k-长DNA子序列频数区划分准则,并详细研究了甚高频数区的n阶零间隔现象,指出n阶零间隔分布就是基因组进化过程所留痕迹的假设,并给出对数频谱图特征的生物学解释。实验发现许多DNA序列频数概率分布近似服从非中心F分布,对于分布呈多峰现象的基因组序列,可采用多个非中心F分布的叠加来拟合。在比较非中心F分布与Gamma分布后,提出一种结合二者在拟合方面具有互补优势的新分布,实验证明这种新分布能够更好地吻合实际DNA序列的频数分布。最后研究了两种特异出现频数(最高出现频数与出现频数为1的k-长子序列个数)与k值的关系,发现不同物种的这两种关系具有良好的一致性。     

Predicting the distribution of the two bark beetles Tomicus destruens and Tomicus piniperda in Europe and the Mediterranean region

• 1 Various factors such as climate and resource availability influence the geographical distributions of organisms. Species sensitive to small temperature variations are known to experience rapid distribution shifts as a result of current global warming, sometimes leading to new threats to agriculture and forests. Tomicus piniperda and Tomicus destruens (Coleoptera, Curculionidae, Scolytinae) cause economic damage to pines in Europe and around the Mediterranean Basin. However, their respective potential distributions have not yet been studied at a large scale. The present study aimed to investigate the influence of climatic and host factors on the geographical distributions of both Tomicus species in Europe and around the Mediterranean Sea, and to establish maps of suitable areas.
• 2 Using 114 published localities where the presence or absence of both species was unambiguously recorded, we gathered WorldClim meteorological records to correlate the occurrence of insects with bioclimatic variables and to build potential distribution maps.
• 3 The two studied Tomicus species presented parapatric distributions and opposite climate demands, with T. destruens occurring in locations with warmer temperatures, whereas T. piniperda occurs under a colder climate. Amongst the investigated climate variables, temperature appeared to be most correlated with both species distributions.
• 4 The potential ranges of both species were further restricted by the availability of pine hosts. It appeared that setting new pine plantations in regions where T. destruens or T. piniperda are still absent could favour a rapid expansion of their distributions. Our data will be useful when aiming to apply management strategies adapted to each species, and to forecast their potential range expansions/contractions as a result of climate warming.

     

Bayesian semiparametric analysis of developmental toxicology data

Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.     

The effect of habitat stability on benthic invertebrate communities: the utility of species abundance distributions

Spatial and temporal patterns in the species abundance distribution of benthic invertebrate communities of 11 freshwater habitats (10 streams and a wind-swept lake shore) were examined with respect to habitat stability. Abundance patterns varied markedly between seasons at most sites. However, mean abundance distributions at 4 of the 5 unstable sites and the 2 most stable sites were dominated by one or two taxa with a large number of rare species, whereas sites of intermediate stability had more equitable distributions. Both the log series and log normal distributions were statistically indistinguishable, at the 5% level, from all the observed mean abundance patterns. In contrast, graphical comparisons of the observed and fitted distributions suggested the log series may be the better fit at most of the unstable sites and the two most stable sites, whereas the more equitable distribution at sites of intermediate stability suggested the log normal distribution was the better fit. If conditions at a site favoured one or two species, either through severe physical conditions, or through competitive superiority in the absence of disturbance then the log series distribution may result. However, if no species in the community was strongly advantaged over others, a log normal distribution should result. Given the discriminating power of the appropriate statistical test it may not, however, be possible to pick up these differences without graphical comparisons as well.     

华中植物区系新资料

该文报道了产鄂西和湘西北的双子叶植物省级分布新记录1个属和8个种。湖北分布新记录有龙珠(Tubocapsicum anomalum)、直梗高山唐松草(Thalictrum alpinum var. elatum)、虫莲(Sanguisorba filiformis)、腺地榆(S. officinalis var. glandulosa)、平叶酸藤子(Embelia undulata)、广西地海椒(Physaliastrum chamaesarachoides)、东北薄荷(Mentha sachalinensis)、黄鼠狼花(Salvia tricuspis),其中龙珠对应的龙珠属(Tubocapsicum)是湖北新记录属;湖南分布新记录有宝兴藨寄生(Gleadovia mupinense)。根据IUCN标准,宝兴藨寄生属濒危(EN)物种。这些新记录的发现丰富了华中植物区系资料,在植物保护方面也有一定意义。     

Oviposition pattern of phytophagous insects: on the importance of host population heterogeneity

Frequency distributions of insect immatures per host are often fitted to contagious distributions, such as the negative binomial, to deduce oviposition pattern. However, different mechanisms can be involved for each theoretical distribution and additional biological information is needed to correctly interpret the fits. We chose the chestnut weevil Curculio elephas, a pest of the European chestnut Castanea sativa, as a model to illustrate the difficulties of inferring oviposition pattern from fits to theoretical distributions and from the variance/mean ratio. From field studies over 13–16 years, we show that 20 out of the 31 yearly distributions available fit a negative binomial and 25 a zero-inflated Poisson (ZIP). No distribution fits a Poisson distribution. The ZIP distribution assumes heterogeneity within the fruit population. There are two categories of host: the first comprises chestnuts unsuitable for weevil oviposition or in excess relative to the number of weevil females, and the second comprises suitable fruits in which oviposition behavior is random. Our results confirm this host heterogeneity. According to the ZIP distribution, the first category of hosts includes on average 74% of the chestnuts. A negative binomial distribution may be generated by either true or false contagion. We show that neither interference between weevil females, nor spatial variation in the infestation rate exist. Consequently, the observed distributions of immatures are not the result of false contagion. Nevertheless, we cannot totally exlude true contagion of immatures. In this paper we discuss the difficulty of testing true contagion in natural conditions. These results show that we cannot systematically conclude in favour of contagion when fitting a distribution such as the negative binomial or when a variance/mean ratio is higher than unity. Received: 22 September 1997 / Accepted: 15 December 1997     

武夷山景区主要景观类型斑块大小分布规律及其等级尺度效应分析

以武夷山风景名胜区为研究对象,运用景观分类生态原则和群落生态学原则,将武夷山风景名胜区划分为10类景观类型,并提取各类型斑块的面积、周长、数量等信息。在此基础上,运用正态分布、对数正态分布、Weibull分布、г-分布、Bata-分布及负指数分布等6个常见的概率分布,分别在3种等级划分条件下,对各景观类型斑块大小分布规律进行研究．结果表明,多数斑块大小服从对数正态分布。少数服从r．分布和Weibull分布,而所有类型的斑块大小均不服从正态分布;对于同一景观类型而言,不同划分等级对其斑块大小的分布规律产生一定的影响,即斑块大小分布存在着等级效应,其中以b等级划分相对比较理想;对不同的景观类型而言,斑块大小分布规律依类型的不同而存在差异,而且就整个景区所有斑块大小分布来说,尚未有一种概率分布能理想地加以刻画;由具有相同分布规律的不同景观类型的斑块构成的整体,其斑块大小分布规律基本保持不变,而由不同分布规律的不同景观类型的斑块构成的整体,其斑块大小分布规律发生变化。     

The influence of coarse‐scale environmental features on current and predicted future distributions of narrow‐range endemic crayfish populations

1. A major limitation to effective management of narrow‐range crayfish populations is the paucity of information on the spatial distribution of crayfish species and a general understanding of the interacting environmental variables that drive current and future potential distributional patterns. 2. Maximum Entropy Species Distribution Modeling Software (MaxEnt) was used to predict the current and future potential distributions of four endemic crayfish species in the Ouachita Mountains. Current distributions were modelled using climate, geology, soils, land use, landform and flow variables thought to be important to lotic crayfish. Potential changes in the distribution were forecast by using models trained on current conditions and projecting onto the landscape predicted under climate‐change scenarios. 3. The modelled distribution of the four species closely resembled the perceived distribution of each species but also predicted populations in streams and catchments where they had not previously been collected. Soils, elevation and winter precipitation and temperature most strongly related to current distributions and represented 65–87% of the predictive power of the models. Model accuracy was high for all models, and model predictions of new populations were verified through additional field sampling. 4. Current models created using two spatial resolutions (1 and 4.5 km²) showed that fine‐resolution data more accurately represented current distributions. For three of the four species, the 1‐km² resolution models resulted in more conservative predictions. However, the modelled distributional extent of Orconectes leptogonopodus was similar regardless of data resolution. Field validations indicated 1‐km² resolution models were more accurate than 4.5‐km² resolution models. 5. Future projected (4.5‐km² resolution models) model distributions indicated three of the four endemic species would have truncated ranges with low occurrence probabilities under the low‐emission scenario, whereas two of four species would be severely restricted in range under moderate–high emissions. Discrepancies in the two emission scenarios probably relate to the exclusion of behavioural adaptations from species‐distribution models. 6. These model predictions illustrate possible impacts of climate change on narrow‐range endemic crayfish populations. The predictions do not account for biotic interactions, migration, local habitat conditions or species adaptation. However, we identified the constraining landscape features acting on these populations that provide a framework for addressing habitat needs at a fine scale and developing targeted and systematic monitoring programmes.     

Climate Change Impacts on Faidherbia albida (Delile) A. Chev. Distribution in Dry Lands of Ethiopia

Given recent and projected climate change, the study of adaptation and mitigation strategies which involve ecologically and economically important plant species is urgently needed. Faidherbia albida (Delile) A. Chev. is a species of both economic and ecological importance. We use 229 locational records gathered in the dry highlands of Ethiopia, nineteen environmental variables and the modelling program MaxEnt to model both the present and possible future distributions of this species. To model future distributions, we used two emission scenarios (Representative Concentration Pathways 2.6 and 8.5) for two time slices (2050 and 2070). Mean temperature of wettest quarter was the major factor which determines the species' potential distribution. Suitable habitat for F. albida under the current climatic conditions is the mid‐highlands. However, its future distributions would shift upwards in elevation and will likely lead to some decrease in suitable areas, especially towards the end of the century. At the same time, however, other areas would become suitable for colonization, so that, overall, the species does not appear to face a significant reduction in distribution within our study region. Future studies should consider the possible effects of climate extremes, further environmental factors and of evolutionary adaptation of the species to new conditions.     

Limits to the estimation of species richness: The use of relative abundance distributions

The present study demonstrates the possibility of estimating species numbers of animal or plant communities from samples using relative abundance distributions. We use log‐abundance–species‐rank order plots and derive two new estimators that are based on log‐series and lognormal distributions. At small to moderate sample sizes these estimators appear to be more precise than previous parametric and nonparametric estimators. We test our estimators using samples from 171 published medium‐sized to large animal and plant communities taken from the literature. By this we show that our new estimators define also limits of precision.     

Maximum-entropy calculation of free energy distributions for two forms of myoglobin

The temperature dependence of the heat capacity of myoglobin depends dramatically on pH. At low pH (near 4.5), there are two weak maxima in the heat capacity at low and intermediate temperatures, respectively, whereas at high pH (near 10.7), there is one strong maximum at high temperature. Using literature data for the low-pH form (Hallerbach and Hinz, 1999) and for the high-pH form (Makhatadze and Privalov, 1995), we applied a recently developed technique (Poland, 2001d) to calculate the free energy distributions for the two forms of the protein. In this method, the temperature dependence of the heat capacity is used to calculate moments of the protein enthalpy distribution function, which in turn, using the maximum-entropy method, are used to construct the actual distribution function. The enthalpy distribution function for a protein gives the fraction of protein molecules in solution having a given value of the enthalpy, which can be interpreted as the probability that a molecule picked at random has a given enthalpy value. Given the enthalpy distribution functions at several temperatures, one can then construct a master free energy function from which the probability distributions at all temperatures can be calculated. For the high-pH form of myoglobin, the enthalpy distribution function that is obtained exhibits bimodal behavior at the temperature corresponding to the maximum in the heat capacity (Poland, 2001a), reflecting the presence of two populations of molecules (native and unfolded). For this form of myoglobin, the temperature evolution of the relative probabilities of the two populations can be obtained in detail from the master free energy function. In contrast, the enthalpy distribution function for the low-pH form of myoglobin does not show any special structure at any temperature. In this form of myoglobin the enthalpy distribution function simply exhibits a single maximum at all temperatures, with the position of the maximum increasing to higher enthalpy values as the temperature is increased, indicating that in this case there is a continuous evolution of species rather than a shift between two distinct population of molecules.     

Symmetric Bernoulli Distributions and Generalized Binomial Distributions

The generalized binomial distribution is defined as the distribution of a sum of symmetrically distributed Bernoulli random variates. Several two-parameter families of generalized binomial distributions have received attention in the literature, including the Polya urn model, the correlated binomial model and the latent variable model. Some properties and limitations of the three distributions are described. An algorithm for maximum likelihood estimation for two-parameter generalized binomial distributions is proposed. The Polya urn model and the latent variable model were found to provide good fits to sub-binomial data given by Parkes. An extension of the latent variable model to incorporate heterogeneous response probabilities is discussed.     

Analytical Quantile Solution for the S‐distribution,Random Number Generation and Statistical Data Modeling

The selection of a specific statistical distribution as a model for describing the population behavior of a given variable is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and selecting the one providing the best fit to the observed data and being the most parsimonious. Alternatively, one can make a choice based on theoretical arguments and simply fit the corresponding parameters to the observed data. In either case, different distributions can give similar results and provide almost equivalent models for a given data set. Model selection can be more complicated when the goal is to describe a trend in the distribution of a given variable. In those cases, changes in shape and skewness are difficult to represent by a single distributional form. As an alternative to the use of complicated families of distributions as models for data, the S‐distribution [Voit, E. O. (1992) Biom. J. 7 , 855–878] provides a highly flexible mathematical form in which the density is defined as a function of the cumulative. S‐distributions can accurately approximate many known continuous and unimodal distributions, preserving the well known limit relationships between them. Besides representing well‐known distributions, S‐distributions provide an infinity of new possibilities that do not correspond with known classical distributions. Although the utility and performance of this general form has been clearly proved in different applications, its definition as a differential equation is a potential drawback for some problems. In this paper we obtain an analytical solution for the quantile equation that highly simplifies the use of S‐distributions. We show the utility of this solution in different applications. After classifying the different qualitative behaviors of the S‐distribution in parameter space, we show how to obtain different S‐distributions that accomplish specific constraints. One of the most interesting cases is the possibility of obtaining distributions that acomplish P(X ≤ X_c) = 0. Then, we demonstrate that the quantile solution facilitates the use of S‐distributions in Monte‐Carlo experiments through the generation of random samples. Finally, we show how to fit an S‐distribution to actual data, so that the resulting distribution can be used as a statistical model for them.     

A frequency distribution approach to hotspot identification

We present a new global method for the identification of hotspots in conservation and ecology. The method is based on the identification of spatial structure properties through cumulative relative frequency distributions curves, and is tested with two case studies, the identification of fish density hotspots and terrestrial vertebrate species diversity hotspots. Results from the frequency distribution method are compared with those from standard techniques among local, partially local and global methods. Our approach offers the main advantage to be independent from the selection of any threshold, neighborhood, or other parameter that affect most of the currently available methods for hotspot analysis. The two case studies show how such elements of arbitrariness of the traditional methods influence both size and location of the identified hotspots, and how this new global method can be used for a more objective selection of hotspots.     

豚草条纹萤叶甲各虫态的空间分布型

豚草条纹萤叶甲Ophraella communa LeSage是恶性入侵豚草(Ambrosia artemisiifolia L.)的天敌,用频次分布拟合和多种聚集指数测度等方法对该叶甲的成虫、幼虫和蛹、卵的空间分布型进行研究。结果表明,豚草条纹萤叶甲卵、幼虫+蛹、成虫的空间分布符合负二项分布,种群个体的空间分布为聚集分布。用几种衡量聚集度的指标,对上述各虫态分布的聚集程度进行测定;然后计算出各虫态田间最适理论抽样数。