We extend the classic sequential stochastic assignment problem to include arrivals of workers. When workers are all of the same type, we show that the socially optimal policy is the same as the individually optimal policy for which workers are given priority according to last come–first served. This result also holds under several variants in the model assumptions. When workers have different types, we show that the socially optimal policy is determined by thresholds such that more valuable jobs are given to more valuable workers, but now the individually optimal policy is no longer socially optimal. We also show that the overall value increases when worker or job values become more variable.

In our article [3] we have found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.

In this article we investigate conditions by a unified method under which the covariances of functions of two adjacent ordered random variables are nonnegative. The main structural results are applied to several kinds of ordered random variable, such as delayed record values, continuous and discrete ℓ∞⩽-spherical order statistics, epoch times of mixed Poisson processes, generalized order statistics, discrete weak record values, and epoch times of modified geometric processes. These applications extend the main results for ordinary order statistics in Qi [28] and for usual record values in Nagaraja and Nevzorov [25].

We consider the problem of optimally maintaining an offshore wind farm in which major components progressively degrade over time due to normal usage and exposure to a randomly varying environment. The turbines exhibit both economic and stochastic dependence due to shared maintenance setup costs and their common environment. Our aim is to identify optimal replacement policies that minimize the expected total discounted setup, replacement, and lost power production costs over an infinite horizon. The problem is formulated using a Markov decision process (MDP) model from which we establish monotonicity of the cost function jointly in the degradation level and environment state and characterize the structure of the optimal replacement policy. For the special case of a two-turbine farm, we prove that the replacement threshold of one turbine depends not only on its own state of degradation but also on the state of degradation of the other turbine in the farm. This result yields a complete characterization of the replacement policy of both turbines by a monotone curve. The policies characterized herein can be used to optimally prescribe timely replacements of major components and suggest when it is most beneficial to share costly maintenance resources.

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.

Alternating renewal processes have been widely used to model social and scientific phenomenal where independent “on” and “off” states alternate. In this paper, we study a model where the value of a process cumulates and declines according to two modes of compound Poisson processes with respect to an underlying alternating renewal process. The model discussed in the present paper can be used as a revenue management model applied to inventory or to finance. The exact distribution of the process is derived as well as the double Laplace transform with respect to the level and time of the process.

This paper studies an optimal deterministic investment problem for a DC pension plan member with inflation risk. We describe the price processes of the inflation-indexed bond and the stock by a continuous diffusion process and a jump diffusion process with random parameters, respectively. The contribution rate linked to the income of the DC plan member is assumed to be a non-Markovian adapted process. Under the mean-variance criterion, we use Malliavin calculus to derive a characterization for the optimal deterministic investment strategy. In some special cases, we obtain the explicit expressions for the optimal deterministic strategies.

It is argued that the analysis of family extinction data that resulted in the claim of a 26-Myr periodicity of mass extinctions was flawed in that it did not allow for the possibility of a symmetric random walk model, which is shown to be perfectly consistent with the data.

Sensitivity analysis is an integral part of virtually every study of system reliability. This paper describes a Monte Carlo sampling plan for estimating this sensitivity in system reliability to changes in component reliabilities. The unique feature of the approach is that sample data collected on K independent replications using a specified component reliability vector p are transformed by an importance function into unbiased estimates of system reliability for each component reliability vector q in a set of vectors Q. Moreover, this importance function together with available prior information about the given system enables one to produce estimates that require considerably less computing time to achieve a specified accuracy for all |Q| reliability estimates than a set of |Q| crude Monte Carlo sampling experiments would require to estimate each of the |Q| system reliabilities separately. As the number of components in the system grows, the relative efficiency continues to favor the proposed method.

The paper shows the intimate relationship between the proposal and the method of control variates. Next, it relates the proposal to the estimation of coefficients in a reliability polynomial and indicates how this concept can be used to improve computing efficiency in certain cases. It also describes a procedure that determines the p vector, to be used in the sampling experiment, that minimizes a bound on the worst-case variance. The paper also derives individual and simultaneous confidence intervals that hold for every fixed sample size K. An example illustrates how the proposal works in an s-t connectedness problem.

The mechanism of the Counter Scheme (CS) has been shown to be an effective statistical approach for the reorganization of linear lists, where the records in the list are referenced independently with a time homogeneous multinomial distribution. In this paper we show that derivative schemes can be used effectively in other contexts as well. Specifically, we consider (a) linear lists that are doubly linked, so that they may be accessed at both ends, (b) multilists, which result from dissecting a linear list into several pieces that are accessed independently and reside in WORM (write-once-read-many) store, and (c) reorganizing a disk, by copying its contents to another disk, so as to minimize the expected seek time required to access a record.

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process, modeled again by a marked point process. Taking into account the presence of catastrophic events, the possibility of common jump times between the risky asset price process and the arrivals process is allowed. By setting and solving a suitable control problem, the characterization of the minimal entropy martingale measure is obtained. In a particular case, a pricing problem is also discussed.

In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed.

Motivated by many applications in production planning, system reliability, queueing networks, and wireless communication, this work is devoted to singularly perturbed Markov chains with finite states. Focusing on nonstationary processes with the inclusion of transient states, asymptotic error bounds of a sequence of suitably scaled occupation measures are derived. The main tools used include martingales and differential equations. The results are useful for analyzing structural properties of the underlying Markov chains and for designing nearly optimal and hierarchical controls of large-scale and complex systems.

Considering the Gaussian noise channel, Costa [4] investigated the concavity of the entropy power when the input signal and noise components are independent. His argument was connected to the first-order derivative of the Fisher information. In real situations, however, the noise can be highly dependent on the main signal. In this paper, we suppose that the input signal and noise variables are dependent. Then, some well-known copula functions are used to define their dependence structure. The first- and second-order derivatives of Fisher information of the model are obtained. Then, by using these derivatives, we will generalize two inequalities based on the Fisher information and a functional that is closely associated to Fisher information for the case when the input signal and noise variables are dependent. We will also show that the previous results for the independent case are recovered as special cases of our result. Several applications are provided to support the usefulness of our results. Finally, the channel capacity of the Gaussian noise channel model with dependent signal and noise is studied.

The minimum expected number of binomial group tests is lower bounded by the cost of a particular Huffman coding problem whose solution is known. Thus, the information lower bound in binomial group testing is improved when the probability that each item is defective is small.

This paper is concerned with overflows in queues fed by Markov fluid input. The results are asymptotic in the number of sources; that is, we let the number of users grow large. The main objectives of this study are to characterize both overflow probability and the “most probable way” in which overflow occurs. Applying large deviations techniques, known results (Weiss, 1986, Advances in Applied Probability 18: 506–532) for exponential on-off sources are extended to general Markov fluid input. Successively, zero, small, and large buffers are treated. Finally, results for multiclass input are given.

In this article, we obtain error bounds for exponential approximations to the classes of weighted residual and equilibrium lifetime distributions with monotone weight functions. These bounds are obtained for the class of distributions with increasing (decreasing) hazard rate and mean residual life functions.

Ranked set sampling (RSS) and some of its variants are sampling designs that are applied widely in different areas. When the underlying population contains different subpopulations, we can use stratified ranked set sampling (SRSS) which combines the advantages of stratification with RSS. In the present paper, we consider the information content of SRSS in terms of extropy measure. Some results using stochastic orders properties are obtained. The effect of imperfect ranking on discrimination information is analytically investigated. It is proved that discrimination information between the perfect SRSS and simple random sampling (SRS) data sets performs better than that of between the imperfect SRSS and SRS data sets.

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

Let F and G be life-length distributions such that F [D over less-than or equals] G. We solve the following problem: How should (X,Y) be generated in order to maximize [hollow letter P](X = Y), under the conditions X [D over equals] F, Y [D over equals] G, and X ≤ Y? We also find a necessary and sufficient condition for the existence of such a maximal coupling with the property that X and Y are independent, conditioned that X < Y. It is pointed out that using familiar Poisson process thinning methods does not produce (X,Y) which maximizes [hollow letter P](X = Y).