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Biometrical Journal (03233847)67(2)
The mean residual life (MRL) function plays an important role in the summary and analysis of survival data. The main advantage of this function is that it summarizes the information in units of time instead of a probability scale, which requires careful interpretation. Ranked set sampling (RSS) is a sampling technique designed for situations, where obtaining precise measurements of sample units is expensive or difficult, but ranking them without referring to their accurate values is cost-effective or easy. However, the practical application of RSS is hindered because each sample unit is required to assign a unique rank. To alleviate this difficulty, Frey developed a novel variation of RSS, called RSS-t, that records and utilizes the tie structure in the ranking process. In this paper, we propose several different nonparametric estimators for the MRL function based on RSS-t. Then, we compare the proposed estimators with their counterparts in simple random sampling (SRS) and RSS, where tie information is not utilized. We also implemented our proposed estimators on a real data set related to patient waiting times for liver transplantation, to show their applicability and efficiency in practice. Our results show that using ties information leads to an improved statistical inference for the MRL function, and therefore a smaller sample size is needed to reach a predetermined precision. © 2025 Wiley-VCH GmbH.
International Journal of Biostatistics (15574679)20(2)pp. 571-583
The mean residual lifetime (MRL) of a unit in a population at a given time t, is the average remaining lifetime among those population units still alive at the time t. In some applications, it is reasonable to assume that MRL function is a decreasing function over time. Thus, one natural way to improve the estimation of MRL function is to use this assumption in estimation process. In this paper, we develop an MRL estimator in ranked set sampling (RSS) which, enjoys the monotonicity property. We prove that it is a strongly uniformly consistent estimator of true MRL function. We also show that the asymptotic distribution of the introduced estimator is the same as the empirical one, and therefore the novel estimator is obtained "free of charge", at least in an asymptotic sense. We then compare the proposed estimator with its competitors in RSS and simple random sampling (SRS) using Monte Carlo simulation. Our simulation results confirm the superiority of the proposed procedure for finite sample sizes. Finally, a real dataset from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) is used to show that the introduced technique can provide more accurate estimates for the average remaining lifetime of patients with breast cancer. © 2024 Walter de Gruyter GmbH, Berlin/Boston.
Scandinavian Journal of Statistics (14679469)51(2)pp. 447-484
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo-likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including Function-on-Scalar regression, functional one-way ANOVA, and equality of covariance operators. © 2023 The Board of the Foundation of the Scandinavian Journal of Statistics.
Statistical Papers (09325026)64(1)pp. 161-177
The mean past lifetime (MPL) is an important tool in reliability and survival analysis for measuring the average time elapsed since the occurrence of an event, under the condition that the event has occurred before a specific time t> 0. This article develops a nonparametric estimator for MPL based on observations collected according to ranked set sampling (RSS) design. It is shown that the proposed estimator is a strongly uniform consistent estimator of MPL. It is also proved that the introduced estimator tends to a Gaussian process under some mild conditions. A Monte Carlo simulation study is employed to evaluate the performance of the proposed estimator with its competitor in simple random sampling (SRS). Our findings show the introduced estimator is more efficient than its counterpart estimator in SRS as long as the quality of ranking is better than random. Finally, an illustrative example is provided to describe the potential application of the developed estimator in assessing the average time between the infection and diagnosis in HIV patients. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability (17480078)237(6)pp. 1100-1113
In the literature of system reliability and other fields related to the time to occurrence of an event, shock models play an important role. In this paper, we assume that a system is subject to shocks that occur according to a counting process describing the number of shocks that arrive during a specified time interval. As the magnitude of the damage imposed to the system by each shock is a crucial parameter to the system’s survival, we investigate some important random variables related to this parameter. A random variable of interest associated with this process is the first time, after a pre-specified time (Formula presented.), at which the amount of a shock damage to the system gets greater than the maximum of damages imposed to the system until time (Formula presented.). We obtain the reliability function of this random variable and investigate various properties of it and some other related random variables. In order to explore further the results, we examine two commonly used processes in the literature, that is, the non-homogeneous Poisson process and the Pólya process. © IMechE 2022.
Journal of Statistical Physics (00224715)189(1)
We study a system of coalescing random walks on the integer lattice Zd in which the walk is oriented in the d-th direction and follows certain specified rules. We first study the geometry of the paths and show that, almost surely, the paths form a graph consisting of just one tree for dimensions d= 2 , 3 and infinitely many disjoint trees for dimensions d≥ 4. Also, there is no bi-infinite path in the graph almost surely for d≥ 2. Subsequently, we prove that for d= 2 the diffusive scaling of this system converges in distribution to the Brownian web. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability (17480078)235(5)pp. 909-922
This article is a study on the reliability characteristics of a system under a failure model called the generalized mixed (Formula presented.) -shock model. We assume that the system is subject to shocks according to a stochastic process. Each shock may cause some damage to the system. The system fails either the magnitude of the damage caused by a shock exceeds a threshold (Formula presented.) or the time between two consecutive shocks is less than a pre-specified threshold (Formula presented.) and simultaneously magnitude of the damage is bigger than a pre-specified critical threshold (Formula presented.) ((Formula presented.)). The survival function and other characteristics of the system lifetime are investigated. By imposing a cost function, we arrive at an optimal replacement policy for the system based on the proposed failure model. Several examples are provided under which we illustrate the theoretical results numerically and graphically. © IMechE 2021.
Computational Statistics and Data Analysis (01679473)135pp. 35-55
The mean residual life (MRL) of a nonnegative random variable X plays an important role in various disciplines such as reliability, survival analysis, and extreme value theory. This paper deals with the problem of estimating the MRL in ranked set sampling (RSS) design. An RSS-based estimator for MRL is proposed and its properties are investigated. For finite sample sizes, a Monte Carlo simulation study is carried out to show that the resulting estimator is more efficient than its counterpart in simple random sampling (SRS) design. It is proved that the proposed estimator asymptotically follows a Gaussian process and its asymptotic variance is no larger than its counterpart in the SRS design, regardless of the quality of ranking. Different methods of constructing a confidence interval for MRL in the RSS and SRS designs are then discussed. It is observed that while both the RSS and SRS-based confidence intervals do not control the nominal confidence level equally well, the RSS-based confidence intervals have generally shorter lengths than those in the SRS scheme. Finally, a potential application in the context of medical studies is presented for illustration purpose. © 2019 Elsevier B.V.
Communications in Statistics - Theory and Methods (1532415X)47(10)pp. 2373-2378
In this note, we derive some mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at time t1 the jth failures has occurred and at time t2 the kth failures (j < k) have not occurred yet. Based on the mixture representations, we then discuss the stochastic comparisons of the conditional residual lifetimes of two coherent systems with i.i.d. components. © 2018 Taylor & Francis Group, LLC.
Panahbehagh, B.,
Bruggemann r., ,
Parvardeh, A.,
Salehi m., M.,
Sabzalian, M.R. Journal of Survey Statistics and Methodology (23250992)6(3)pp. 285-305
In ranked-set sampling, the restriction of selecting just one individual from each set may require too many sets. We propose a new version of ranked-set sampling that relaxes this restriction. Our new design uses stratified sampling in which ranked-set sampling is used to form the strata. Simulations, and a real case study on medicinal flowers, show that this design can be more precise and less costly than previous designs. © The Author 2017. Published by Oxford University Press on behalf of the American Association for Public Opinion Research. All rights reserved.
Communications in Statistics - Theory and Methods (3610926)46(7)pp. 3401-3410
In this paper, we obtain a mixture representation for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under double monitoring. We suppose that at time t1, j components have failed while at time t2 the system is still alive. Based on these mixture representation, we then study stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components. © 2017 Taylor & Francis Group, LLC.
Parvardeh, A.,
Mohammadi jouzdani n., ,
Mahmoodi s., ,
Soltani a.r., A.R. Journal of Mathematical Analysis and Applications (0022247X)449(1)pp. 756-768
We let B be a separable Banach space, and let {Zn} be a sequence of independent and identically distributed random elements in B. Then we prove that for a given strongly periodic sequence of bounded linear operators {ρn}, the order one autoregressive system equations Xn=ρnXn−1+Zn,n in set on integers, possesses a unique almost sure strictly periodically correlated solution; under E[log+‖Z0‖]<∞, which appears to be necessary as well. We proceed on to derive the limiting distribution of ∑n=1NXn that appears to be a Gaussian distribution on B. We also provide interesting examples and observations. © 2016 Elsevier Inc.
Statistical Papers (9325026)56(1)pp. 205-215
A measure used in reliability and survival analysis is mean past lifetime (MPL). In this paper, we study the asymptotic strong uniform behavior and the weak convergence of estimation ofMPL function.We also investigate the Hadamard differentiability of MPL at the fixed time and obtain asymptotic distribution of its estimate by using the functional delta method again. © 2013, Springer-Verlag Berlin Heidelberg
Statistics and Probability Letters (1677152)102pp. 51-60
In this note, we study the system lifetime mixed δ-shock models. In this model, the system fails when the time between two successive shocks is smaller than a critical threshold δ, or the magnitude of the shock (the cumulative magnitude of shocks) is larger than another critical threshold γ. We then obtain the survival function of the system under these new shock models. © 2015 Elsevier B.V.
Journal of Applied Probability (219002)51(4)pp. 990-998
In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components. © Applied Probability Trust 2014.
Bulletin of the Iranian Mathematical Society (10186301)40(2)pp. 339-355
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a periodiccyclic flow. © 2014 Iranian Mathematical Society.
Parvardeh, A.,
Panahbehagh, B.,
Salehi m., M.,
Brown, J.,
Smith, D.R. Bulletin Of The Iranian Mathematical Society (1017060X)39(3)pp. 529-557
We extend the method of adaptive two-stage sequen-tial sampling to include designs where there is more than one crite-ria used in deciding on the allocation of additional sampling effort. These criteria, or conditions, can be a measure of the target popula-tion, or a measure of some related population. We develop Murthy estimator for the design that is unbiased estimators for the pop-ulation mean, and propose another, more efficient, estimator. We investigate asymptotic properties of this estimator. We use a sim-ulation study to investigate design properties of the multi-criteria adaptive stratified sequential sampling scheme and also some esti-mator properties under the design. ©2013 Iranian Mathematical Society.
Statistics and Probability Letters (1677152)83(12)pp. 2664-2672
In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k - 1 (. j < k) components have failed by time t. Based on these mixture representations, we then discuss stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components. © 2013 Elsevier B.V.
Salehi m., M.,
Panahbehagh, B.,
Parvardeh, A.,
Smith, D.R.,
Lei, Y. Environmental and Ecological Statistics (13528505)20(4)pp. 571-590
Adaptive two-stage sequential sampling (ATSSS) design was developed to observe more rare units and gain higher efficiency, in the sense of having a smaller variance estimator, than conventional sampling designs with equal effort for rare and spatially cluster populations. For certain rare populations, incorporating auxiliary variables into a sampling design can further improve the observation of rare units and increase efficiency. In this article, we develop regression-type estimators for ATSSS so that auxiliary variables can be incorporated into the ATSSS design when warranted. Simulation studies on two populations show that the regression-type estimators can significantly increase the efficiency of ATSSS and the detection of more rare units as compared to conventional sampling counterparts. Simulation of sampling of desert shrubs in Inner Mongolia (one of the two populations studied) showed that by incorporating a GIS auxiliary variable into ATSSS with the regression estimators resulted in a gain in efficiency over ATSSS without the auxiliary variable. Further, we found that the use of the GIS auxiliary variable in a conventional two-stage design with a regression estimator did not show a gain in efficiency. © 2013 Springer Science+Business Media New York.
Theory of Probability and its Applications (0040585X)50(3)pp. 448-462
A simple random measure is a finite sum of random measures with disjoint supports. A type of simple random measure which is induced by a multivariate random measure (Φ1, . . . , Φm) and measurable mappings T1, . . . , Tm is introduced and studied. Interestingly it gives rise to introducing a class of processes, called simple, that include stationary processes and discrete time periodically correlated processes. This study involves spectral domain and time domain characterizations and simulation. The role of spectral kernels in analysis of nonstationary processes is also discussed. © 2006 Society for Industrial and Applied Mathematics.
Stochastic Processes and their Applications (3044149)115(11)pp. 1838-1859
The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric α-stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable processes that are classified as mixed moving average, harmonizable and of a third kind. The techniques are based on presenting the flow and its cocycle that govern the spectral representation of the process, using the Hopf decomposition and specifying the harmonizable component. © 2005 Elsevier B.V. All rights reserved.
