We apply Stein’s method for probabilistic approximation by a compound geometric distribution, with applications to Markov chain hitting times and sequence patterns. Bounds on our Stein operator are found using a complex analytical approach based on generating functions and Cauchy’s formula.

Background Due to the industrial significance, elongational viscosity of polymeric liquids has been widely investigated. In particular, strain hardening, which is the deviation of the elongational viscosity from the linear viscoelastic envelope, has been of industrial and scientific interest because polymeric liquids exhibiting strain hardening are suitable for processing technologies with elon...

Let {Xi, i ≥ 1} denote a sequence of {0, 1}-variables and suppose that the sequence forms a Markov Chain. In the paper we study the number of successes Sn = X1 + X2 + · · · + Xn and we study the number of experiments Y (r) up to the r-th success. In the i.i.d. case Sn has a binomial distribution and Y (r) has a negative binomial distribution and the asymptotic behaviour is well known. In the mo...

Supply chain management (SCM) addresses the management of materials and information across the entire chain from suppliers to producers, distributors, retailers, and customer. The theory of supply chain management suggests that lead time reduction is a pioneer to the use of market mediation to reduce transaction uncertainty in the chain, which can be conceptualized as the primary goal of supply...

This study utilizes the Markov-chain mixture distribution model (MCM) for very short term load forecasting of residential electricity consumption. The is used to forecast one step ahead half hour resolution consumption data from Australia. results are compared with Quantile Regression (QR) and Persistence Ensemble (PeEn) as advanced simple benchmark models. were in terms reliability, reliabilit...

Accurate reconstruction of species trees often relies on the quality input gene estimated from molecular sequences. Previous studies suggested that if sequence length is fixed, maximum likelihood may produce biased which subsequently mislead inference trees. Two key questions need to be answered in this context: what are scenarios result consistently trees? and for those scenarios, there any re...

The design and configuration of an effective supply chain has been widely recognised as being of fundamental importance to the business performance of all companies within the present competitive market. In supply chain structure, outbound physical distribution channel can be regarded as the key stage which will meet the customers’ demand and requirements directly. This paper mainly involves st...