Supplies from developing countries: Optimal order quantities under loss risks

When raw material suppliers of a global supply chain are situated in developing countries, not only will there be long lead times but there could also be a possibility of material losses in transit. The magnitude of the losses will be uncertain and can be significant. We consider the optimization of order quantity decisions in such situations. The long lead times imply that we need to take into account the uncertainty in finished goods demands for which the raw materials are to be ordered. The order quantities have to be optimized carefully as they determine the “real options” that become available later in production plans. Using data from the plywood industry and using stochastic programming we demonstrate a method for solving such problems. The method combines simulation and optimization. An interesting observation we make is that the optimal order quantity of a material need not be monotonic in expected loss of that material. In addition, we offer explanations as to why the expected loss need not be monotonic.     

On the Cycle-Transitivity of the Dice Model

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and ukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.     

Reversible jump Markov chain Monte Carlo algorithms for Bayesian variable selection in logistic mixed models

In this article, to reduce computational load in performing Bayesian variable selection, we used a variant of reversible jump Markov chain Monte Carlo methods, and the Holmes and Held (HH) algorithm, to sample model index variables in logistic mixed models involving a large number of explanatory variables. Furthermore, we proposed a simple proposal distribution for model index variables, and used a simulation study and real example to compare the performance of the HH algorithm with our proposed and existing proposal distributions. The results show that the HH algorithm with our proposed proposal distribution is a computationally efficient and reliable selection method.     

Kumaraswamy Marshall-Olkin Exponential distribution

In this paper, a new generalization of the Kumaraswamy distribution namely, the Kumaraswamy Marshall-Olkin Exponential distribution (KwMOE) is introduced and studied. Various properties are explored. The structural analysis includes various aspects such as limiting behaviour, shape properties, moments, quantiles, mean deviation, Renyi entropy, order statistics and stochastic ordering. Some useful characterizations of the family are also obtained. The method of maximum likelihood is used to estimate the model parameters. Monte Carlo simulation study is being conducted. An application to a real data set is presented for illustrative purposes.     

Some Results Based on a Version of the Generalized Dynamic Entropies

We propose new dynamic measures of uncertainty based on the notion of generalized dynamic entropy introduced in Di Crescenzo and Longobardi (2006). These can uniquely determine distribution functions in continuous and discrete cases, and the characterizations of some well-known distributions are provided. We also define some orderings and aging notions based on the generalized dynamic measures, and prove some of their properties, obtaining as corollaries results that have recently appeared in the literature.     

Stochastic Bounds with a Low Rank Decomposition

We investigate how we can bound a discrete time Markov chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the article, we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.     

Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.     

Estimation of error probabilities in stochastic dominance

The process of using data to infer the existence of stochastic dominance is subject to sampling error. Kroll and Levy (1980), among others, have presented simulation results for several normal and lognormal distributions which show high error probabilities for a wide range of parameter values. This paper continues this line of research and uses simulation to estimate error probabilities. Distributions considered are a pair of normals and a pair of lognormals. Analysis of these distributions is made computationally feasible through theoretical results which reduce the number of parameters of the pair of distributions from four to two.     

Generalized integer-valued random coefficient for a first order structure autoregressive (RCINAR) process

A random coefficient autoregressive process for count data based on a generalized thinning operator is presented. Existence and weak stationarity conditions for these models are established. For the particular case of the (generalized) binomial thinning, it is proved that the necessary and sufficient conditions for weak stationarity are the same as those for continuous-valued AR(1) processes. These kinds of processes are appropriate for modelling non-linear integer-valued time series. They allow for over-dispersion and are appropriate when including covariates. Model parameters estimators are calculated and their properties studied analytically and/or through simulation.     

Asymptotic posterior normality for multiparameter problems

For asymptotic posterior normality in the one-parameter cases, Weng [2003. On Stein's identity for posterior normality. Statist. Sinica 13, 495–506] proposed to use a version of Stein's Identity to write the posterior expectations for functions of a normalized quantity in a form that is more transparent and can be easily analyzed. In the present paper we extend this approach to the multi-parameter cases and compare our conditions with earlier work. Three examples are used to illustrate the application of this method.