A Class of Lindley and Weibull Distributions

In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.

Empirical Bayesian Approach to Testing Homogeneity of Several Means of Inflated Poisson Distributions (IPD)

Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.

Vegetation structure,dominance patterns and height growth in an Afromontane forest,Southern Africa

Information on forest structure is fundamentally important to track successional vegetation dynamics for efficient forest management.This study reports on vegetation characteristics,dominance patterns and species height growth in a northern mistbelt forest type in South Africa.Common alpha-diversity indices(species richness and Shannon-Weiner diversity),structural vegetation parameters(tree density and basal area),and species importance value index were used.Size class distribution and height-diameter allometry were further examined for the overall stand and most important species.Stem densities(472.0±43.5 and 605.3±28.1 trees ha^-1 for C 5 cm to\10 cm and C 10 cm dbh(diameter at breast height)classes,respectively)and basal area values(1.99±0.19 and 48.07±3.46 m^2 ha^-1,respectively)are comparable to other Afromontane forests in East Africa.The overall stand showed an inverted-J shaped distribution pattern which is a typical feature of stand size class distribution in most natural forests.Most ecologically important species also exhibited an inverted-J shaped distribution pattern,suggesting good regeneration and recruitment potential.There were significant differences in species on height,reflecting species-specific height growth patterns,possibly a result of intrinsic growth potential and competitive interactions.The present study suggests that conservation and management policies,including protection of surrounding land uses against fire,contribute to maintaining a successful recovery of these forests.However,it should be noted that these forests may be experiencing relatively slow dynamic flux as a result of the overmature state of some trees with several years under relatively strict protection.

Spatial analysis and structure of a cross-timber stand in the TallGrass Prairie Preserve (Pawhuska, Oklahoma)

I analyzed the spatial distribution and structure of trees in a cross timber forest in the Tallgrass Prairie Preserve （Pawhuska, Oklahoma, USA）. I mapped and measured diameter of all stems, saplings （〉1.5 m tall） and dead trees in a 4-ha plot. The stand was dominated by Quercus stellata and Q. marilandica. In total, I mapped 7,636 trees, consisting of 6,785 Q. stellata, 846 Q. marilandica, 2 Celtis occidentalis, 1 Fraxinus pensilvanica and 2 Prunus americana. For saplings, I mapped 54 Q. stellata and 21 Q. marilandica. The size class distribution of the two dominant species did not differ. The dominant mortality class was “standing dead”, while I only found saplings less than 2 m tall. The spatial distribution of the species indicated segregation in the use of the environment, generating a clumped univariate distribution of stems of the same species within radii of 30 m, but repulsion outside 30 m. This segregation can be explained by the different ecological requirements of each species.

Diversity and Structure of Miombo Woodlands in Mozambique Using a Range of Sampling Sizes

Forest assessments are essential to understand the tree population structure and diversity status of forests and to provide information for biodiversity recovery planning. Unfortunately, the majority of Miombo woodlands in Mozambique lack of inventory data, and consequently are often insufficient for management. This study aimed to assess the species richness, diversity and structure of Miombo woodlands using a range of sampling sizes in Mocuba district, Mozambique. Plant inventory was carried out in 128 systematically selected sample plots in 71.6 ha, which was divided into eight treatments, i.e., TI： 0.1 ha; T2：0.25 ha; T3：0.375 ha; T4：0.5 ha; T5：0.625 ha; T6：0.75 ha; T7：0.875 ha; T8：1.0 ha, with 16 repetitions. All stems _〉 10 cm diameter at breast height, and species name to evaluate the floristic composition, richness of tree species, diversity and diameter distribution were recorded. A total of 36,535 individuals were recorded, belonging 124 species, 83 genera and representing 31 botanical families. The most important species was the Brachystegia spiciformis Benth. and the richest botanical family was Fabaceae. The forest showed an average of 517 ＋ 85 trees/ha, and high species diversity and evenness. Analysis of covariance shows that the intercepts and slope of exponential function for diameter distribution are not significantly different for the eight treatments. Compared with the entire composite forest, inventory means were accurately estimated and size class distributions were well represented for plots 〈 0.25 ha, for selecting an efficient sampling design suited to forest characteristics and the inventory＇s purpose.

Problems of Personal Income Tax System and Suggestions： from Function of Tax Adjustment Income Gap

China has a late start in personal income tax, and for many years through six times of revision, it still fails to really achieve the purpose of narrowing the gap between the rich and the poor and adjusting income distribution. What follows is an analysis of personal adjustment tax income from the proportion of Gini coefficient, Engels coefficient and salaried class of personal income tax, and an explanation of problems and countermeasures of salaried class expense deduction standard, tax rate design, high-income crowd tax regulation.

FG-SMOTE:Fuzzy-based Gaussian synthetic minority oversampling with deep belief networks classifier for skewed class distribution

Purpose-Adequate resources for learning and training the data are an important constraint to develop an efficient classifier with outstanding performance.The data usually follows a biased distribution of classes that reflects an unequal distribution of classes within a dataset.This issue is known as the imbalance problem,which is one of the most common issues occurring in real-time applications.Learning of imbalanced datasets is a ubiquitous challenge in the field of data mining.Imbalanced data degrades the performance of the classifier by producing inaccurate results.Design/methodology/approach-In the proposed work,a novel fuzzy-based Gaussian synthetic minority oversampling(FG-SMOTE)algorithm is proposed to process the imbalanced data.The mechanism of the Gaussian SMOTE technique is based on finding the nearest neighbour concept to balance the ratio between minority and majority class datasets.The ratio of the datasets belonging to the minority and majority class is balanced using a fuzzy-based Levenshtein distance measure technique.Findings-The performance and the accuracy of the proposed algorithm is evaluated using the deep belief networks classifier and the results showed the efficiency of the fuzzy-based Gaussian SMOTE technique achieved an AUC:93.7%.F1 Score Prediction:94.2%,Geometric Mean Score:93.6%predicted from confusion matrix.Research limitations/implications-The proposed research still retains some of the challenges that need to be focused such as application FG-SMOTE to multiclass imbalanced dataset and to evaluate dataset imbalance problem in a distributed environment.Originality/value-The proposed algorithm fundamentally solves the data imbalance issues and challenges involved in handling the imbalanced data.FG-SMOTE has aided in balancing minority and majority class datasets.

Tail behavior of supremum of a random walk when Cramer＇s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.

ON THE COMPLETION TIME AND THE INTERRUPTION TIME OF A JOB PROCESSED ON AN UNRELIABLE MACHINE

This paper considers the completion time and the interruption time of a job processed on an unreliable machine. By using the general theory of stochastic orderings, we obtain the closure properties of the distribution of the completion time and the interruption time on L^+ and PH life distribution classes. We get an exponential bound for the tail probability of the interruption time.