Sujit K. Basu

On a nonparametric family of life distributions and its dual

Abstract In this paper, we discuss a nonparametric family of life distributions (called the NWBUE family) which includes the IDMRL class of distributions introduced by Guess, Hollander and Proschan as well as all BFR distributions. We prove two inequalities which are then used to obtain bounds for moments of a NWBUE life distribution. The bounds thus obtained are shown to be related to the moments of an appropriate negative exponential distribution, and a characterization of the exponential distribution is derived as a consequence. Closure under weak convergence and the equivalence of weak convergence and moment convergence in the NWBUE family are established under mild conditions. Similar properties in respect of the dual family comprising of NBWUE distributions have also been explored.

An optimal ordering policy for situations with uncertainty in supply

A one-period inventory model where supply is a random variable with mean proportional to the quantity ordered has been considered. Under new better than used in expectation assumption on the supply variable, a strategy which maximizes a minimum profit has been suggested. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been proposed and almost sure convergence of this estimate to its true value with increasing sample size has been established.

Characterizing the Exponential Law Under Laplace Order Domination

Interesting characterizations of the exponential distribution have been obtained in classes of life distributions important in reliability theory. The results strengthen some of the analogous conclusions already existing in the literature. AMS (1991) Subject Classification No. Primary 62NOS: Secondaey 90825. 60F99.

Testing Exponentiality Against Laplace Order Dominance

We present a statistical procedure to test that a life distribution belongs to the class of exponential distributions against that it belongs to a class of alternatives based on the Laplace transform. The test has been shown to be consistent and the asymptotic distribution of the test statistic has been obtained. The performance of the test against various classes of alternatives has been studied by means of Monte Carlo simulation. An interesting characterization theorem for exponentials, which motivates our test procedure, has been proved.

On some properties of the bathtub failure rate family of life distributions

In this paper, some of the basic issues concerning the bathtub failure rate (BFR) life distributions, thus far unresolved, have been investigated. Specifically, exponential bounds have been obtained for the survival function as well as the moments of a BFR distribution. Closure properties of the BFR family under the formation of coherent systems, convolutions and mixtures have been dealt with. Closure of the BFR class under the formation of limits in distribution and the equivalence of weak convergence and convergence of moment sequences have been established.

Asymptotic normality of the estimated optimal order quantity for one-period inventories with supply uncertainty

A one‐period inventory situation where the supply is an NBUE random variable with mean proportional to the quantity ordered has been considered. The optimal exponential order quantity, which maximizes the minimum profit obtainable in the NBUE class of supply distributions, is a function of the demand distribution function. Here we show that an estimator of the maximin order quantity, which is already known to converge almost surely to its true value, converges also in distribution to an appropriate normal law with increasing sample size.

An Optimum Ordering Policy and its Estimation in a Two-Supplier Inventory Model with Uncertainties in Supply

We consider a single-item one-period inventory model where the market demand is assumed to be random and the item under consideration is obtained from two suppliers who also supply random amounts with means equal to the order placed to the supplier concerned. Under new better than used in expectation (NBUE) assumption on the supply distributions, possibly different, a strategy which maximizes a minimum profit has been proposed. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been obtained and strong consistency of the suggested estimator established. AMS (2000) Subject Classification: Primary 90B05; Secondary 62G99, 60F15.

“Residual Life Time at Great Age” Revisited 1

We follow up on results on the unit exponential law as the weak limit of residual life time normalized by the mean residual life time function and investigate further on the connection between such weak covergence and convergence of its suitable moment sequence.

Optimal Ordering Strategy Under Risk and its Nonparametric Estimation

SYNOPTIC ABSTRACTWe consider the problem of nonparametric estimation of the optimal ordering strategy in a one-period inventory situation where both the supply and the (customer) demand are random variables with unknown distributions. Almost sure convergence of the proposed estimator to its true value has been established.

Optimum Ordering Policy in a Bicomponent Inventory Model : Statistical Aspects

ABSTRACT: This paper considers a situation where the manufacturer of a two‐component product receives supplies of the two eomponents presumably from two different sources each supplying components of one variety. Under NBUE assumption on both the supply random variables, a strategy which maximizes the minimum expected profit in a one‐period inventory model, with uncertainty in demand, has been explored. An estimator for this maximin order quantity whenever the demand distribution is unknown has been proposed and almost sure convergence· of this estimator to its true value has been established. Further asymptotic results helpful in testing or interval estimation problems concerning the maximin order quantity have also been derived. AMS 1980 Subject Classification: 90B05, 60F05.