On testing independence with right truncated data

Cataloged from PDF version of article.Inference with bivariate data gained considerable interest recently, See eg.[1],[10],[12]. All of these studies howrver consider estimation of the bivariate distribution function under various bivariate censoring models. Recently (:iirler[7,8] considered estimation of the bivariate distribution and the hazard functions under trunc.atlon/censoring models. The purpose of this study is to investigate procedures for testing the independence of I hc components of the bivariate vector for truncated data. To this end, further properties of the bivariate functrouals introduced in GiirleQ] are elaborated. Two alternative methods for hypothesis testing are suggested aud some large sample properties are derived. The procedures suggested in this paper are applicable to left/right. truncated and left truncated right censored data. However to keep the presentation simple we ~~oufinr t.hr discussion to the right truncated case. Also, to avoid technicalities, it is assumed that all the univariat.e and the bivariate distribution functions are absolutely continuous admitting densities

On the use of phase-type distributions for inventory management with supply disruptions

Cataloged from PDF version of article.Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase-type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long-run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen. Copyright (C) 2011 John Wiley & Sons, Ltd

Variance of the bivariate density estimator for left truncated right censored data

Cataloged from PDF version of article.In this study the variance of the bivariate kernel density estimators for the left truncated and right censored (LTRC) observations are considered. In LTRC models, the complete observation of the variable Y is prevented by the truncating variable T and the censoring variable C. Consequently, one observes the i.i.d, samples from the triplets (T,Z,delta) only if T less than or equal to Z, Z=min(Y, C) and delta is one if Z=Y and zero otherwise. Gurler and Prewitt (1997, submitted for publication) consider the estimation of the bivariate density function via nonparametric kernel methods and establish an i.i.d. representation of their estimators. Asymptotic variance of the i.i.d, part of their representation is developed in this paper. Application of the results are also discussed for the data-driven and the least-squares cross validation bandwidth choice procedures. (C) 1999 published by Elsevier Science B.V. All rights reserved

Adjusted Hazard Rate Estimator Based on a Known Censoring Probability

Cataloged from PDF version of article.In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques

Optimal bundle formation and pricing of two products with limited stock

Cataloged from PDF version of article.In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable. © 2009 Elsevier B.V. All rights reserved

Bundle pricing of inventories with stochastic demand

Cataloged from PDF version of article.We consider a retailer selling a fixed inventory of two perishable products over a finite horizon. Assuming Poisson arrivals and a bivariate reservation price distribution, we determine the optimal product and bundle prices that maximize the expected revenue. Our results indicate that the performances of mixed bundling, pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels. Bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels. When the starting inventory levels are equal and in excess of average demand, most of the benefits of bundling can be achieved through pure bundling. However, the mixed bundling strategy dominates the other two when the starting inventory levels are not equal. We also observe that an incorrect modeling of the reservation prices may lead to significant losses. The model is extended to allow for price changes during the selling horizon. It is shown that offering price bundles mid-season may be more effective than changing individual product prices. 2008 Elsevier B.V. All rights reserved

Centralized and decentralized management of groundwater with multiple users

Cataloged from PDF version of article.In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems. 2011 Elsevier B.V. All rights reserved

A Continuous Review Replenishment-Disposal Policy for an Inventory System with autonomous supply and fixed disposal costs

Cataloged from PDF version of article.In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment-disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability. (C) 2007 Elsevier B.V. All rights reserved

On pricing of perishable assets with menu costs

Cataloged from PDF version of article.We consider dynamic pricing of perishable assets in the presence of price-sensitive renewal demand processes. Unlike the existing works in the literature, we explicitly incorporate non-negligible price change costs which reflects the revenue management practice more realistically. These costs are also known as menu costs in the economic literature. The objective is to maximize the discounted expected profit for an initial inventory of Q items by determining the selling prices dynamically. We employ a dynamic programming approach and formulate a model that captures the price– demand relationship. We establish some theoretical results on the properties of the problem at hand. Specifically, we establish the sufficient conditions under which the within-period profit is concave in the selling price and in the remaining shelf life and, furthermore, show the structure of the myopically and asymptotically optimal pricing policy. In a numerical study, we investigate the impact of various system parameters and, in particular, the existence of menu costs, on pricing decisions. We observe that ignoring menu costs may be significantly misleading for the implementation of revenue management. We also propose four implementable policy heuristics and examine their performances. Our findings support some results previously obtained in settings with continuous pricing and negligible price change costs; and, contradict some others. & 2009 Published by Elsevier B.V

Weak and strong quantile representations for randomly truncated data with applications

Cataloged from PDF version of article.Suppose that we observe bivariate data (X,. q) only when Y, < Xi (left truncation). Denote with F the marginal d.f. of the X’s In this paper we derive a Bahadur-type representation for the quantile function of the pertaining product-limit estimator of F. As an application we obtain confidence intervals and bands for quantiles of F