Abstract:
Normal variance-mean mixtures encompass a large family of useful distributions such as the generalized hyperbolic distribution, which itself includes the Student t, Laplace, hyperbolic, normal inverse Gaussian, and variance gamma distributions as special cases. We study shape properties of normal variance-mean mixtures, in both the univariate and multivariate cases, and determine conditions for unimodality and log-concavity of the density functions. This leads to a short proof of the unimodality of all generalized hyperbolic densities. We also interpret such results in practical terms and discuss discrete analogues.

Abstract:
As the world map which is published on the net by State Bureau of Surveying and Mapping has no the concrete projection parameters and the normal and inverse transformation formulae,it is difficult to project the geo-information to the map.We derived the formulae of the normal and inverse solution of equivalent difference latitude parallel polyconic projection.Throught choosing the reference points,and computing the projection parameters from the coordinate values of reference points,people can make the transformation of geo-information according to the normal and inverse transformation formulae,and project the dots,lines or panels to the map easily.

Abstract:
Based on the data of mean air temperature in January, July and whole year of 1978,1984,1990,1996 in Northeastern and Central China, the comparison of precisions of spatial methods were conducted using direct interpolation methods including Inverse distance weighted and Ordinary Kriging, three dimension-second order trend surface analysis and spatial interpolation method, spatial climatic value integrating with the multi-annual deviation from normal interpolation methods and spatial climatic value integrating with trend simulating to the multi-annual deviation from normal combining with residual interpolation methods. Taking mean absolute error, mean relative error and crossing validation as evaluation criterion, it is concluded that as far as mean air temperature is concerned, the method of spatial climatic value integrating with the multi-annual deviation from normal interpolation by IDW is not only a convenient but also relatively precise spatial method with smaller error in Northeastern and Central China based on multi-annual mean air temperature raster database. Furthermore, three dimension-second order trend surface analysis and spatial interpolation method, which is suitable for interpolate to multi-annual mean climatic data, is unsuitable for the interpolation of short time serial climatic data. It is worthily noticed that above methods cannot play a good role to all of climatic factors because the diversity exists between different climatic factors for the difference of spatial-temporal distribution, continuity and local natural conditions.

Abstract:
The calculation of the mean difference for
the lognormal distribution involves several hard integrals featuring the error
function. In this paper, considering two particular cases of an integral of the
exponential function for the complement to one of？the error functions, and
using various symmetries, we have achieved the result of an extremely simple
and useful formula of the mean difference for the lognormal distribution.

Abstract:
The flame emission spectrometry was applied to detect the distribution of excited radicals in two types CH4/O2 coflow jet diffusion flames (normal and inverse diffusion flames). Combining the image analysis along with the spectrometry, the chemiluminescence and structure characteristics of these diffusion flames were investigated. The results show that the inverse diffusion flame (IDF) with relatively high inlet oxygen velocity is composed of two regions: a bright base and a tower on top of the base, which is quite different from the normal diffusion flame (NDF). The flame is divided into two regions along the flame axis based on maximum OH* position (Region I: initial reaction zone; Region II: further oxidation zone). The degree of the further oxidization taking place in Region II is obvious in accordance with OH* distribution, which is the main difference in reaction zone between fuel-rich condition and fuel-lean condition for NDFs. For IDFs, the change of OH* distribution with increasing equivalence O/C ratio ( ) in Region II is not conspicuous. More OH* and CH* are generated in IDFs, due to the inner high-speed O2 flow promoting the mixing of fuel and oxygen to a certain extent. 1. Introduction Most of the practical combustion systems such as coal gasifiers, gas turbine engines and industrial stoves. employ diffusion combustion because of its better flame stability, safety, and wide operating range as compared to premixed combustion [1]. According to the feeding pattern of the fuel and oxidizer, there are two types of diffusion flames: normal diffusion flame (NDF) and inverse diffusion flame (IDF). The IDF is a special flame with an inner oxidizer jet surrounded by an outer fuel jet, with less soot produced as compared to NDF [2], so that the application of IDF in industry is becoming more and more widespread. In some processes of coal gasification, the combustion of inner oxygen and fuel from the annulus forms the IDF. In the coke oven gas autothermal reforming technology, the flame type is a typical IDF [3]. In recent times, there has been a growing interest in researching of IDF and its difference with NDF. The first detailed investigation was performed by Wu [4] for laminar methane IDF stabilized in a simple coaxial burner. He identified six different regimes of IDF and found that IDF and NDF had almost the same visible appearance in the confined space. The comparative study on hydrogen IDF and NDF performed by Takagi et al. [5] revealed the occurrence of higher flame tip temperature in IDF than NDF. They defined a parameter called H2 ratio to

Abstract:
We examine the efficiency of the mean deviation and Gini's mean difference (the mean of all pairwise distances). Our findings support the viewpoint that Gini's mean difference combines the advantages of the mean deviation and the standard deviation.

Abstract:
A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from an iterative Markov chain Monte Carlo (MCMC) scheme that addresses this problem and it can be viewed as a generalization of a recently proposed relevant model. Conditions are provided under which it is proved that the scheme converges to a unique fixed point. Finally, the theoretical results are also supported by computer simulations, which also show the rapid convergence of the method to a solution vector that is very close to the mean of the truncated normal distribution under study.

Abstract:
In the present article we derive an explicit expression for the trun- cated mean and variance for the multivariate normal distribution with ar- bitrary rectangular double truncation. We use the moment generating ap- proach of Tallis (1961) and extend it to general {\mu}, {\Sigma} and all combinations of truncation. As part of the solution we also give a formula for the bivari- ate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after trunca- tion. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.

Abstract:
We propose approximations to the normal distribution function and to its inverse function using single polynomials in each case. The absolute error of these approximations is significantly less than those of other approximations available in the literature. We compare all the polynomial approximations empirically by calculating their respective percentage absolute relative errors.