A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non‐adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non‐adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.     

Progressively Type-II censored conditionally N-ordered statistics from a unified elliptically contoured copula

Progressively Type-II censored conditionally N-ordered statistics (PCCOS-N) arising from iid random vectors X_i = (X¹_i, X²_i, …, X_i^p), i = 1, 2…, n, were investigated by Bairamov (2006 Bairamov, I. (2006). Progressive Type II censored order statistics for multivariate observations. J. Mult. Anal. 97:797–809.[Crossref], [Web of Science ®] , [Google Scholar]), with respect to the magnitudes of N(X_i), i = 1, 2, …, n, where N( · ) is a p-variate measurable function defined on the support set of X₁ satisfying certain regularity conditions and N(X_i) denotes the lifetime of the random vector X_i, i = 1, …, n. Under the PCCOS-N sampling scheme, n independent units are placed on a life-test and after the ith failure, R_i (i = 1, …, m) of the surviving units are removed at random from the remaining observations. In this article, we consider PCCOS-N arising from a vector with identical as well as non identical dependent components, jointly distributed according to a unified elliptically contoured copula (PCCOSDUECC-N). Results established here contain the previous results as particular cases. Illustrative examples and simulation studies show that PCCOSDUECC-N enables us to analyze the lifetime of several systems, including repairable systems and systems with standby components, more efficiently than PCCOS-N.     

Reliability analysis of consecutive k-out-of-n systems with non-identical components lifetimes

In recent years, the study of reliability properties of consecutive k-out-of-n systems has attracted a great deal of attention from both theoretical and practical perspectives. In this paper we consider linear and circular consecutive k-out-of-n systems. It is assumed that lifetimes of components of the systems are independent but their probability distributions are non-identical. We study the reliability properties of the residual lifetimes of such systems under the condition that at least (n−r+1), r≤n, components of the system are operating. We also investigate the probability that a specific number of components of the above-mentioned system operate at time t, t>0, under the condition that the system is alive at time t.     

An adaptive allocation sampling design for which the conventional stratified estimator is an appropriate estimator

Adaptive allocations in stratified sampling design are suitable for studying Biological and Environmental populations. Biologists tend to use the conventional stratified estimator for an adaptive allocation sampling design in spite of its adaptive nature. In this paper, we have introduced an adaptive allocation sampling design for which the conventional stratified estimator has some desired statistical properties. We conduct a simulation study on a real population. The results show that the conventional stratified estimator for the introduced adaptive allocation sampling design is more efficient than other available estimators.     

Comparison of two sampling schemes for generating record-breaking data from the proportional hazard rate models

ABSTRACT

In this article, we consider a sampling scheme in record-breaking data set-up, as record ranked set sampling. We compare the proposed sampling with the well-known sampling scheme in record values known as inverse sampling scheme when the underlying distribution follows the proportional hazard rate model. Various point estimators are obtained in each sampling schemes and compared with respect to mean squared error and Pitman measure of closeness criteria. It is observed in most of the situations that the new sampling scheme provides more efficient estimators than their counterparts. Finally, one data set has been analyzed for illustrative purposes.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Robust finite mixture modeling of multivariate unrestricted skew-normal generalized hyperbolic distributions

In this paper, we introduce an unrestricted skew-normal generalized hyperbolic (SUNGH) distribution for use in finite mixture modeling or clustering problems. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. We illustrate the flexibility of the proposed class of distributions in a mixture modeling context using a Bayesian framework and assess the performance using simulated and real data.