On Characterizing Some Discrete Distributions by a Conditional Distribution and a Regression Function

In this paper we consider characterizations of the binomial, negative binomial, hypergeometric, negative hypergeometric, multinomial and multivariate hypergeometric distributions, by linear regression of one random variable (vector) on the other and the conditional distribution of the other random variable (vector) given the first. It is also indicated how these results can be used in genetics.     

Bivariate Modified Power Series Distribution Some Properties,Estimation and Applications

The class of bivariate modified power series probability distribution (BMPSD) has been defined by P(X = x, Y=y) =a(x, y) (g(?₁ ?₂))^x (h(?₁, ?₂))^xwhere a(x,y) is a sub-set of the Cartesian product of the set of non-negative integers and g(?₁, ?₂), h(?₁ ?₂) and f(?₁, (?₁, ?₂) are positive finite and successively differentiable functions of ?₁and ?₂. It includes a very large number of well known probability distributions. The recurrence relations for central moments and factorial moments have been determined. Also, the M.L. estimators for ?₁ and ?₂ and their asymptotic biases and variances are obtained. Some important properties are discussed. The results of an BMPSD have been applied to derive the corresponding results for the bivariate generalized negative bino-mial distribution and the bivariate Lagrangian Poisson distribution.     

A Variation of the Method of Translation to Generate Bivariate and Multivariate Survival Distributions with Competing Risk or Reliability Applications

In the present paper, a variation of the methode of translation is discussed to generate bivariate or multivariate survival distributions starting a given bivariate or multivariate distribution which is not necessarily a life distribution. The new distribution has been called the dual of the given distribution. The duals of several bivariate and multivariate famílies of distributions are obtained, such as FRECHET'S , FARLIE -GUMBEL -MORGENSTERN'S , MARDIA'S and PLACKETT'S , among others. A necessary and sufficient condition is given for a bivariate distribution to be its own dual. Thus the present paper generates several survival distributions in addition to what are already available in the literature. These have important applications in competing risk theory or reliability of engineering systems.     

On Some Stochastic Problems in Epidemiology under the Binomial Damage Model

The present paper discusses some probability problems in epidemiology in which a community is divided into two parts by means of the binomial damage model. The community size N is an integer-valued random v?ariable and p denotes the incidence rate of a certain disease such that conditional on N=n, the number B of infected individuals in the community follows a binomial distribution with parameters n and p. Let C denote the number of the susceptibles, where B + C = N. Probabilities are found of the events, such as, only half the community is hit by the disease, or there are n more susceptibles than are infected for n=0, 1, 2,…, or the susceptibles exceed the infected, or the susceptibles exceed (m-1) times the number of infected individuals for m = 2, 3,…, etc. These probabilities play an useful role when a public health official wishes to ascertain that only a given proportion 1/m of the community is infected with the disease. Only the cases when the community size N follows the geometric, negative binomial or FISHER'S logarithmic series distributions are considered with the mathematics being manageable.     

改性瓜尔胶的制备及其絮凝性能的研究

对瓜尔胶进行铵基化阳离子改性,得到一种天然絮凝剂.研究了改性瓜尔胶絮凝剂处理污水的效果,以及pH值、反应温度、粘度、取代度等因素对高岭土悬浮液絮凝效果的影响.结果表明,粘度为3 000～5 000mPa·s,阳离子取代度为13%的改性瓜胶对高岭土悬浮液有较好的絮凝效果,在胶加入量为0.2 mL/L,搅拌速度为500r/min、搅拌时间为15 min等条件下,沉降15 min可达到彻底絮凝和澄清.此外,该絮凝剂基本不受温度和水质pH影响,且絮凝性能明显优于聚丙烯酰胺、硫酸铝以及三氯化铁等絮凝剂,因而在工业废水处理中具有良好的应用前景.     

On the Probabilities of Obtaining Negative Estimates of Genetic Variance Components

This paper derives the probabilities of obtaining negative estimates of additive and dominance genetic variances when one uses the traditional weighted least square method for estimating genetic variances as given in MATHER and JINKS (1971). The model considered involves P₁, P₂, F₂, B₁ (Backcross to P₁) and B₂ (Backcross to P₂). The results are derived under the ordinary assumptions as made in the genetic literatures. It is shown that unless the genetic effects are very large and environmental effects small, the probabilities of obtaining negative estimates of additive and dominance variances are in general quite large.     

On the difference between gauss-markov and least squares estimates

For the usual full rank univariate least squares regression model y = XB + e, E(e) = 0, E(ee) = A, the equality of the estimates occurs when B-B^* = (XA^?1X)^?1XA^-1y-(XX)^?1Xy = 0. A necessary and sufficient condition for this equality is that A has some N - k + 1 roots equal where N is the rank of A and k is the rank of X.     

Some Applications of the Family of Discrete Exponential Distributions in Biology and Toxicology

In this paper the relationship between the number of males and females in a community, between the number of boys and girls in a family, between the number of animals trapped and untrapped in an animal experiment, between the number of infected and uninfected in an epidemiological study, between the number of mutagens and non-mutagens in a given sample of toxicological experiments, and others, is studied. The general expression for the correlation coefficient, ?, is obtained when N, the community size N, has a discrete exponential family distribution recently studied by Janardan (1980). This is then specialized to some well known discrete distributions.     

A Class of Distributions in the First Emptiness of a Semi-Infinite Reservoir

This paper considers the probability distribution of the volume of a certain substance (e.g. river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi-infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time. A few moments of the distribution have been computed. A generalized gamma, and a generalized exponential distributions as particular cases are also discussed. Some possible applications of the generalized negative exponential distribution have been mentioned. These distributions are in fact the continuous analogues of the discrete LAGRANGE distributions recently considered by JAIN and others.     

Seasonal dynamics, dispersion, sequential sampling plans and treatment thresholds for the citrus leafminer, Phyllocnistis citrella Stainton (Lepidoptera: Gracillariidae), in a mature lemon block in coastal New South Wales, Australia

Abstract  Studies of citrus leafminer in a coastal orchard in NSW, Australia indicated that an increase in abundance to about one mine per flush was followed during the midseason flush by a rapid increase in population that was related to an increase in the percentage of leaves infested within flushes and the number of mines per leaf. The fits of frequency distributions and Iwao's patchiness regression indicated that populations were highly contagious initially, and as the exponent k of the negative binomial distribution increased with increasing population density, the distribution approached random. Concurrently, the coefficient of variation of mines per flush (which was strongly related to the proportion of un-infested flushes) decreased to about unity as the proportion of un-infested flushes reached zero and fell further as the number of mines per flush increased. Both numerative and binomial sequential sampling plans were developed using a decision threshold based on 1.2 mines per flush. The binomial sampling plan was based on a closely fitting model of the functional relationship between mean density and proportion of infested flushes. Functional relationships using the parameters determined from Iwao's patchiness regression and Taylor's power law were equally satisfactory, and one based on the negative binomial model also fitted well, but the Poisson model did not. The three best fitting models indicated that a decision threshold of 1.2 mines per flush was equivalent to 50% of flushes infested. From a practical point of view, the transition from 25% infestation of flushes through 50% is so rapid that it may be prudent to take action when the 25% level is reached; otherwise, the 50% may be passed before the crop is checked again. For valuable nursery stock should infestation be detected in spring, it may be advisable to apply prophylactic treatment as the midseason flush starts.     

Cloud frequency correlates to plant species composition in the high Andes of Ecuador

Two data sets representing atmospheric moisture are available for the high Andes of Ecuador, (i) cloud frequency obtained from weather satellites, and (ii) interpolated rainfall estimates obtained from global climate observations. We analyzed their correlation to vascular plant species composition at 18 Ecuadorian superpáramo study sites. Of particular interest was whether cloud frequency could be used as a proxy for precipitation. Cloud frequency had distinct seasonal and spatial variation among the sites. The spatial gradient of cloudiness was strongest during June–August and weakest around the equinoctials. Interpolated rainfall estimates also showed seasonal and spatial variation among the sites, but there was no correlation between them and cloudiness. Cloud frequency during June–August was the only significant variable in the canonical correspondence analysis (CCA) of the species composition, whereas rainfall estimates, geology, presence of glaciers, and size and altitudinal range of the superpáramos were not significant. When the spatial components were filtered out from the species composition data by employing partial CCA, cloud frequency during December–February became the only significant variable. Our results suggest that cloud frequency data may be a useful tool in mountain ecology research, serving as an indicator of habitat humidity when exact precipitation data are lacking.     

Discrete Cilia Modelling with Singularity Distributions: Application to the Embryonic Node and the Airway Surface Liquid

We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous ‘singularity models’ is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a ‘posterior tilt,’ and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 μm/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this technique to various other biological problems, particularly in the reproductive system.     

On the Bond-angle Distributions in Liquids and Liquid Solutions

Bond-angle distributions are used for the study of local orientational order in liquid systems. Bond-angles between a central particle and particles in both the first and second coordination shells are considered. Molecular dynamics calculations are carried out for determining the bond-angle distributions in a Lennard Jones liquid. The resulting distributions are compared with those obtained from stochastic simulations of a subset of atoms (solute) of the same system (solution). Although the radial distribution functions from the two simulations are in agreement, the bond-angle distributions show noticeable difference. Computer simulation findings are compared with results obtained by using both the superposition and convolution approximations. The reliability of the generalized Langevin dynamics simulation method is discussed.     

Effect of habitat disturbance on pollination biology of the columnar cactus Stenocereus quevedonis at landscape‐level in central Mexico

Stenocereus quevedonis (‘pitire’) is a columnar cactus endemic to central Mexico, grown for its edible fruit. Phenology, pollination biology and behaviour of flower visitors of this species were compared in six conserved and disturbed sites, hypothesising that: (i) pitire pollination is self‐incompatible, requiring animal vectors; (ii) higher incidence of radiation on plants in cleared forest may lead to a higher number of flowers per pitire plant and longer blooming season, and disturbing and differential spatial availability of flower resources may determine differential attraction of pollinators to conserved and disturbed areas; (iii) if pitire pollination system is specialised, reproductive success would decrease with pollinator scarcity, or other species may substitute for main pollinators. In all sites, pitire reproduction started in January, flowering peak occurring in April, anthesis duration was 15 h and predominantly nocturnal (9 h), pollen was released at 23:00 h, nectar was produced throughout anthesis, and breeding system was self‐incompatible. Flower production per plant was similar in disturbed and conserved sites, but flower availability was higher (because of higher tree density) and longer in disturbed sites. Pollination is nocturnal, the most frequent legitimate pollinator being the bat Leptonycteris yerbabuenae; diurnal pollination is rare but possible, carried out by bee species. Fruit and seed set in control and nocturnal pollination treatments at disturbed sites were higher than in conserved sites. Frequency of L. yerbabuenae visits was similar among site types, but more visits of complementary nocturnal and diurnal pollinators were recorded in disturbed sites, which could explain differences in reproductive success.     

Vegetation and soil seed bank of successional stages in tropical lowland deciduous forest

Abstract. We studied vegetation structure and soil seed bank composition in different successional stages of secondary lowland tropical deciduous forest in Yucatán, Mexico. The series of study sites includes: slashed (S), slashed-and-burned (SB), and regenerating for 1, 6, 10, 15, 30, 40 and 100 yr. Species richness (S = 42 - 65), evenness (E = 0.32 - 0.38), and diversity (H' = 1.2 - 1.6) do not vary much as the forest grows older. 20 species of shrubs and trees were present in at least six of the seven regrowth years studied; 10 of these account for more than 50% of the total density values per regrowth year. These species dominate the vegetation due to their capacity to withstand repeated fire and felling. One third of the individuals sampled had regenerated from coppiced shoots. Species composition little resembles that in earlier accounts. The area is now largely covered by young regrowth stages (1 - 20 yr). Species constituting the original woody structure of the mature forest are rare or absent due to the lack of seed sources and failure of dispersal (which is due to limited dispersal capacities), lack of dispersal agents, or long distances. Herbs were the most important life form in the soil seed banks; only one tree species was found. The number of viable seeds varied between sampled areas: 70/m² in the 40 yr-old, to 1 815/m² in the slashed-and-burned (SB). The vegetation of S- and SB-areas was the same, but the number of viable seeds germinating in SB was twice the number in S; the number of species in the seed bank is the same for both areas. We speculate that fire modifies species dominance early in succession, allowing seeds of some species to germinate in great numbers.