Bayesian inference for zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables

Abstract

In the fields of internet financial transactions and reliability engineering, there could be more zero and one observations simultaneously. In this paper, considering that it is beyond the range where the conventional model can fit, zero-and-one-inflated geometric distribution regression model is proposed. Ingeniously introducing Pólya-Gamma latent variables in the Bayesian inference, posterior sampling with high-dimensional parameters is converted to latent variables sampling and posterior sampling with lower-dimensional parameters, respectively. Circumventing the need for Metropolis-Hastings sampling, the sample with higher sampling efficiency is obtained. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed method, research shows that zero-and-one-inflated geometric distribution regression model using Pólya-Gamma latent variables can achieve better fitting results.     

Time‐change models for asymmetric processes

Many records in environmental sciences exhibit asymmetric trajectories. The physical mechanisms behind these records may lead for example to sample paths with different characteristics at high and low levels (up–down asymmetries) or in the ascending and descending phases leading to time irreversibility (front–back asymmetries). Such features are important for many applications, and there is a need for simple and tractable models that can reproduce them. In this paper, we explore original time‐change models where the clock is a stochastic process that depends on the observed trajectory. The ergodicity of the proposed model is established under general conditions, and this result is used to develop nonparametric estimation procedures based on the joint distribution of the process and its derivative. The methodology is illustrated on meteorological and oceanographic data sets. We show that, combined with a marginal transformation, the proposed methodology is able to reproduce important characteristics of the data set such as marginal distributions, up‐crossing intensity, and up–down and front–back asymmetries.     

A reflected feature space for CART

We present an algorithm for learning oblique decision trees, called HHCART(G). Our decision tree combines learning concepts from two classification trees, HHCART and Geometric Decision Tree (GDT). HHCART(G) is a simplified HHCART algorithm that uses linear structure in the training examples, captured by a modified GDT angle bisector, to define splitting directions. At each node, we reflect the training examples with respect to the modified angle bisector to align this linear structure with the coordinate axes. Searching axis parallel splits in this reflected feature space provides an efficient and effective way of finding oblique splits in the original feature space. Our method is much simpler than HHCART because it only considers one reflected feature space for node splitting. HHCART considers multiple reflected feature spaces for node splitting making it more computationally intensive to build. Experimental results show that HHCART(G) is an effective classifier, producing compact trees with similar or better results than several other decision trees, including GDT and HHCART trees.     

民生工程建设综合评价研究

民生问题是构建和谐社会的关键,也是政府工作的基本着力点。在前期研究构建的指标体系的基础上,运用拉开档次评价法和逐层序关系分析法对我国31个省市自2006－2012年的民生工程建设状况进行了动态综合评价,并用时序几何平均算子（TOWGA）进行了二次加权得到综合评价的总排名,最后对各地区的排序变化进行归纳、分析。     

Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

A new generalization of the Weibull-geometric distribution with bathtub failure rate

In this paper, the researchers attempt to introduce a new generalization of the Weibull-geometric distribution. The failure rate function of the new model is found to be increasing, decreasing, upside-down bathtub, and bathtub-shaped. The researchers obtained the new model by compounding Weibull distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains some previously known lifetime distributions as well as a new one. Some basic distributional properties and moments of the new model are discussed. Estimation of the parameters is illustrated and the model with two known real data sets is examined.     

Hazard functions and life distributions in discrete time

The problem of studying lifelength distributions in discrete time is considered for certain forms of hazard functions. A class of life distributions that consists of the geometric, the Waring and the negative hypergeometric distributions is shown to result when the hazard function is inversely proportional to some linear function of time.     

Generalized RCINAR(1) Process with Signed Thinning Operator

A generalized random coefficient first-order integer-valued autoregressive process with signed thinning operator is introduced, this kind of process is appropriate for modeling negative integer-valued time series. Strict stationarity and ergodicity of process are established. Estimators of the parameters of interest are derived and their properties are studied via simulation. At last, we use bootstrap method in the real data analysis.     

Global convergence of the log-concave MLE when the true distribution is geometric

Let X₁, …, X_n be i.i.d. from a discrete probability mass function (pmf) p. In Balabdaoui et al. [(2013), ‘Asymptotic Distribution of the Discrete Log-Concave mle and Some Applications’, JRSS-B, in press], the pointwise limit distribution of the log-concave maximum-likelihood estimator (MLE) was derived in both the well- and misspecified settings. In the well-specified setting, the geometric distribution was excluded, classified as being degenerate. In this article, we establish the global asymptotic theory of the log-concave MLE of a geometric pmf in all ?_q distances for q∈{1, 2, …}∪{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric.     

关于抛物线与相交直线围成的弓形面积初等数学解法的探讨

文章运用两种巧妙的分割和利用无究递缩等比数列求和公式等初等数学知识，求出了抛物线与相交直线围成的弓形面积计算公式。