Parvardeh, A.,
Mohammadi jouzdani n., ,
Mahmoodi s., ,
Soltani a.r., A.R. Publication Date: 2017
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.
Publication Date: 2017
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.
Publication Date: 2015
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.
Publication Date: 2015
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
Publication Date: 2014
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.
Publication Date: 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.
Behboudi z., Z.,
Mohtashami borzadaran g.r., G.R.,
Asadi, M. Publication Date: 2023
Applied Stochastic Models in Business and Industry (15264025)39(3)pp. 333-351
This article investigates an optimal preventive standby activation policy for an m-out-of-n redundant system. We assume that for such a system, which starts operating at time t = 0, a standby component will be activated at either the failure time of the system or at a predetermined time tau, whichever occurs first. We first obtain the system reliability function under this switching policy as a function of tau. Then, we investigate the optimal switching time tau so that the mean time to failure of the system is maximized. The results indicate that the existence of an optimal value of tau ,depends on the lifetime of the standby redundancy and its virtual age in the standby state. Some illustrative examples are presented to examine the theoretical outcomes.
Publication Date: 2023
Applied Stochastic Models in Business and Industry (15264025)39(1)pp. 4-53
In reliability engineering literature, a large number of research papers on optimal preventive maintenance (PM) of technical systems (networks) have appeared based on preliminary many different approaches. According to the existing literature on PM strategies, the authors have considered two scenarios for the component failures of the system. The first scenario assumes that the components of the system fail due to aging, while the second scenario assumes the system fails according to the fatal shocks arriving at the system from external or internal sources. This article reviews different approaches on the optimal strategies proposed in the literature on the optimal maintenance of multi-component coherent systems. The emphasis of the article is on PM models given in the literature whose optimization criteria (cost function and stationary availability) are developed by using the signature-based (survival signature-based) reliability of the system lifetime. The notions of signature and survival signature, defined for systems consisting of one type or multiple types of components, respectively, are powerful tools assessing the reliability and stochastic properties of coherent systems. After giving an overview of the research works on age-based PM models of one-unit systems and k-out-of-n systems, we provide a more detailed review of recent results on the signature-based and survival signature-based PM models of complex systems. In order to illustrate the theoretical results on different proposed PM models, we examine two real examples of coherent systems both numerically and graphically.
Publication Date: 2021
IISE TRANSACTIONS (24725854)53(11)pp. 1266-1280
We propose optimal preventive maintenance strategies for n-component coherent systems. We assume that in the early time of the system operation all failed components are repaired, such that the state of a failed component gets back to a working state, worse than that of prior to failure. To model this repair action, we utilize a counting process on the interval (0, tau], known as the generalized Polya process (which subsumes the non-homogeneous Poisson process as a special case). Two generalized Polya process-based repair strategies are proposed. The criteria to be optimized are the cost function formulated based on the repair costs of the components/system, and the system availability, to obtain the optimal time of preventive maintenance of the system. To illustrate the theoretical results, two coherent systems are studied for which the optimal preventive maintenance times are explored under different conditions.
Publication Date: 2023
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION (03610918)54pp. 1587-1600
The probability density function of the multivariate unrestricted skew-normal (SUN) distribution, corresponding to a screened normal density, allow to modeling skewness and kurtosis in data in terms of a skewness parameter vector and a truncation parameter matrix. These parameters are related to the shape and heavy-tails of the density. In this article, we present the Expectation/Conditional Maximization (ECM) algorithm for the SUN distribution based on a hierarchical stochastic representation. In addition, behavior of ECM algorithm's steps is measured using an information theoretic approach based on Jeffrey's divergence and related homogeneity test. Usefulness of the proposed method is illustrated by an application to Chilean economic perception data.
Publication Date: 2022
Medical Journal Of The Islamic Republic Of Iran (10161430)36(1)
Background: Reliance heavily on out-of-pocket (OOP) payments, including informal payments (IPs), has undesired effects on financial risk protection and access to care. While a significant share of total health expenditure is spent on outpatient services, there is scant evidence of the patient's amount paid informally in outpatient services. Such evidence is available for inpatient services, showing the high prevalence of informal payments, ranging from 14 to 48% in the whole hospital. This study aimed to investigate the extent of OOP and IPs for outpatient services in Iran. Methods: A secondary data analysis of the 2015 IR Iran's Utilization of Healthcare Services (IrUHS) survey was conducted. A sample of 11,782 individuals with basic health insurance who were visited at least once by a physician in two private and public health care centers was included in this analysis. The percentage of OOP was determined and compared with the defined copayment (30%). The frequency of IPs was determined regarding the number of individuals who paid more than the defined copayments. The Mann-Whitney test also investigated the relationships between OOP percentage and IPs frequency with demographic variables. Results: The share that insured patients in Iran pay for a general practitioner (GP) visit was 38% in public versus 61% in the private sector, while for a specialist practitioner visit, the figures were 80% and 96%, respectively, which is higher than defined copayment (30%). This share was significantly higher in females, urban areas, highly educated people, private service providers, and specialist visits. The frequency of IPs, who paid more than the defined copayments, was 73% for a GP in public versus 86% in the private sector, while for a specialist practitioner visit, these were 90% and 93%, respectively. Conclusion: Informal patient payments for outpatient services are prevalent in Iran. Hence, more interventions are required to eliminate or control the IPs in outpatient services, particularly in the private sector. In this regard, making a well-regulated market, reinforcing the referral system, and developing an equity-oriented essential health services package would be fundamental © Iran University of Medical Sciences
Publication Date: 2021
Iranian Journal of Science and Technology, Transaction A: Science (10286276)45(3)pp. 1005-1014
The macroscopic behavior of networks, when facing random removal of nodes or edges, can be described as an inverse percolation process in a random graph. To determine whether a network remains operational when its elements (nodes or edges) fail at random, a “network robustness” criterion is used as a probabilistic measure. In this paper, we used percolation theory to assess this criterion for a network subjected to random failures of its elements. We then mapped the random failures process of the network into an inverse percolation problem. After that, based on the threshold for which the connectivity disappears, we assessed network robustness. Also, to demonstrate our method, we studied the robustness of systems that can be modeled as general inhomogeneous random graphs as well as scale-free random graphs. © 2021, Shiraz University.
Publication Date: 2021
Statistics and Applications (24547395)19(1)pp. 443-451
In recent years there has been a vast amount of work to model the spread of rumour. Here we review some of these mathematical models and present some of the main results. © 2021, Society of Statistics, Computer and Applications. All rights reserved.
Publication Date: 2020
Journal of the Iranian Statistical Society (17264057)19(1)pp. 69-83
In this paper, we study an (n-k + 1)-out-of-n system by adopting their components to be statistically independent though nonidentically distributed. By assuming that at least m components at a fixed time have failed while the system is still working, we obtain the mixture representation of survival function for a quantity called the conditional inactivity time of failed components in the system. Moreover, this quantity for (n-k + 1)-out-of-n system, in one sample with respect to k and m and in two samples, are stochastically compared. © 2020 Iranian Statistical Society.
Publication Date: 2019
Journal of Statistical Physics (00224715)174(4)pp. 935-952
Junior et al. (J Appl Probab 48:624–636, 2011) studied a model to understand the spread of a rumour. Their model consists of individuals situated at the integer points of the line N. An individual at the origin 0 starts a rumour and passes it to all individuals in the interval [0 , R] , where R is a non-negative random variable. An individual located at i in this interval receives the rumour and transmits it further among individuals in [i, i+ Ri] where R and Ri are i.i.d. random variables. The rumour spreads in this manner. An alternate model considers individuals seeking to find the rumour from individuals who have already heard it. For this s/he asks individuals to the left of her/him and lying in an interval of a random size. We study these two models, when the individuals are more sceptical and they transmit or accept the rumour only if they receive it from at least two different sources. In stochastic geometry the equivalent of this rumour process is the study of coverage of the space Nd by random sets. Our study here extends the study of coverage of space and considers the case when each vertex of Nd is covered by at least two distinct random sets. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Publication Date: 2018
Iranian Journal of Science and Technology, Transaction A: Science (10286276)42(4)pp. 2183-2187
In this paper, we study the rate of convergence of the connectivity threshold of random geometric graphs when the underlying distribution of the vertices has no density. We consider n i.i.d. skew generalized Cantor distributed points on [0, 1] and we study the connectivity threshold of a random geometric graph that is built on these points. We show that for this graph, the connectivity threshold converges almost surely to a constant, similar result as in case of symmetric generalized Cantor distributed. We also study the rate of the convergence of this threshold in terms of the L1 norm. © 2017, Shiraz University.
Publication Date: 2015
Annals of Applied Probability (10505164)25(2)pp. 663-674
In this work we consider a simple SIR infection spread model on a finite population of n agents represented by a finite graph G. Starting with a fixed set of initial infected vertices the infection spreads in discrete time steps, where each infected vertex tries to infect its neighbors with a fixed probability β ∈ (0, 1), independently of others. It is assumed that each infected vertex dies out after an unit time and the process continues till all infected vertices die out. This model was first studied by [Ann. Appl. Probab. 18 (2008) 359-378]. In this work we find a simple lower bound on the expected number of ever infected vertices using breath-first search algorithm and show that it asymptotically performs better for a fairly large class of graphs than the upper bounds obtained in [Ann. Appl. Probab. 18 (2008) 359-378]. As a by product we also derive the asymptotic value of the expected number of the ever infected vertices when the underlying graph is the random r-regular graph and β < 1/r-1. © Institute of Mathematical Statistics, 2015.
Publication Date: 2014
Journal of Applied Probability (00219002)51(1)pp. 106-117
In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F. © Applied Probability Trust 2014.
Publication Date: 2012
Statistics and Probability Letters (01677152)82(12)pp. 2103-2107
For the connectivity of random geometric graphs, where there is no density for the underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show that for such a random geometric graph, the connectivity threshold, R n, converges almost surely to a constant 1-2φ where 0<φ<1/2, which for the standard Cantor distribution is 1/3. We also show that {norm of matrix}Rn-(1-2φ){norm of matrix}1~2C(φ)n-1/dφ where C(φ)>0 is a constant and d φ{colon equals}-log2/logφ is the Hausdorff dimension of the generalized Cantor set with parameter φ. © 2012 Elsevier B.V..
Publication Date: 2025
Computational Statistics (09434062)40(5)pp. 2729-2748
It is a common challenge in medical field to obtain the prevalence of a specific disease within a given population. To tackle this problem, researchers usually draw a random sample from the target population to obtain an accurate estimate of the proportion of diseased people. However, some limitations may occur in practice due to constraints, such as complexity or cost. In these situations, some alternative sampling techniques are needed to achieve precision with smaller sample sizes. One such approach is Neoteric Ranked Set Sampling (NRSS), which is a variation of Ranked Set Sampling (RSS) design. NRSS scheme involves selecting sample units using a rank-based method that incorporates auxiliary information to obtain a more informative sample. In this article, we focus on the problem of estimating the population proportion using NRSS. We develop an estimator for the population proportion using the NRSS design and establish some of its properties. We employ Monte Carlo simulations to compare the proposed estimator with competitors in Simple Random Sampling (SRS) and RSS designs. Our results demonstrate that statistical inference based on the introduced estimator can be significantly more efficient than its competitors in RSS and SRS designs. Finally, to demonstrate the effectiveness of the proposed procedure in estimating breast cancer prevalence within the target population, we apply it to analyze Wisconsin Breast Cancer data. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Publication Date: 2025
Statistics (02331888)
This research investigates the construction of regression models for scenarios in which the response variable is inflated at specific points. To address this, we propose a comprehensive family of inflated distributions, which encompasses virtually all standard inflated distributions as special cases. The proposed family of distributions is applicable when the variable of interest is discrete, continuous, or a combination of both. We discuss parameter estimation, develop a regression model using the introduced family of distributions, and formulate an expectation-maximization (EM) algorithm to determine the maximum likelihood estimators of the proposed regression model. Additionally, we develop a general likelihood ratio test for the regression parameters. Finally, in two simulation scenarios and two real data sets, (obtained from the US National Center for Health Statistics (NCHS) and the residents of Olmsted County aged 50 or older), we analyse the performance of the proposed model. © 2025 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2024
Environmental and Ecological Statistics (13528505)31(4)pp. 1039-1062
The volume under the receiver operating characteristic (ROC) surface (VUS) is a natural generalization of a classical tool, the area under the ROC curve from a disease with two statuses (e.g., healthy and diseased) to a disease with a three-class status (e.g., healthy, intermediate, and diseased) for evaluating the effectiveness of a continuous biomarker in discriminating the disease status. In this work, we discuss the problem of estimating VUS using ranked set sampling (RSS), a cost-efficient alternative to simple random sampling (SRS), which is applicable in situations in which the actual quantification of the biomarker is hard, time-consuming, costly or tedious but a small number of sample units can still be ordered without referring to their precise values. We develop several nonparametric estimators when SRS or RSS design is applied to each of the healthy, intermediate and diseased subpopulations. We study the properties of the proposed estimators, including unbiasedness, variance expression, asymptotic normality, and efficiency. Specifically, we show that the introduced estimators are at least as efficient as their SRS counterparts and often far more efficient under a large class of imperfect ranking models. Lastly, to demonstrate the applicability and efficiency of the introduced procedures in an environmental context, we apply them to a real environmental dataset, utilizing three of its five classes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Publication Date: 2024
Journal of Applied Statistics (02664763)51(13)pp. 2512-2528
The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2022
Statistical Papers (09325026)63(6)pp. 1777-1799
Ranked set sampling (RSS) utilizes auxiliary information on the variable of interest so as to assist the experimenter in acquiring an informative sample from the population. The resulting sample has a stratified structure, and often improves statistical inference with respect to the simple random sample of comparable size. In RSS literature, there are some goodness-of-fit tests based on the empirical estimators of the in-stratum cumulative distribution functions (CDFs). Motivated by the fact that the in-stratum CDFs in RSS can be expressed as functions of the population CDF, some new tests are developed and their asymptotic properties are explored. An extensive simulation study is performed to evaluate properties of different testing procedures when the parent distribution is normal. It turns out that the proposed tests can be considerably more powerful than their contenders in many situations. An application in the context of fishery is also provided. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Publication Date: 2022
Statistical Methods in Medical Research (09622802)31(8)pp. 1500-1514
In medical research, the receiver operating characteristic curve is widely used to evaluate accuracy of a continuous biomarker. The area under this curve is known as an index for overall performance of the biomarker. This article develops three new estimators of the area under the receiver operating characteristic curve in ranked set sampling. The first estimator is obtained under normality assumption. The two other estimators are constructed by applying a Box–Cox transformation on data, and then using either a parametric estimator or a kernel-density-based estimator. A simulation study is carried out to compare the proposed estimators with those available in the literature. It emerges that the new estimators offer some advantages in specific situations. Application of the methods is demonstrated using real data in the context of medicine. © The Author(s) 2022.
Publication Date: 2022
Soft Computing (14327643)26(7)pp. 3161-3170
It is highly important for governments and health organizations to monitor the prevalence of breast cancer as a leading source of cancer-related death among women. However, the accurate diagnosis of this disease is expensive, especially in developing countries. This article concerns a cost-efficient method for estimating prevalence of breast cancer, when diagnosis is based on a comprehensive biopsy procedure. Multistage ranked set sampling (MSRSS) is utilized to develop a proportion estimator. This design employs imprecise rankings based on some visually assessed cytological covariates, so as to provide the experimenter with a more informative sample. Theoretical properties of the proposed estimator are explored. Evidence from numerical studies is reported. The developed procedure can be substantially more efficient than its competitor in simple random sampling (SRS). In some situations, the proportion estimation in MSRSS needs around 76% fewer observations than that in SRS, given a precision level. Thus, using MSRSS may lead to a considerable reduction in cost with respect to SRS. In many medical studies, e.g., diagnosing breast cancer based on a full biopsy procedure, exact quantification is difficult (costly and/or time-consuming), but the potential sample units can be ranked fairly accurately without actual measurements. In this setup, multistage ranked set sampling is an appropriate design for developing cost-efficient statistical methods. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
