Bounds for the Joint Survival and Incidence Functions Through Coherent System Data

1997 ◽  
Vol 29 (2) ◽  
pp. 478-497 ◽  
Author(s):  
J. V. Deshpande ◽  
S. R. Karia
Keyword(s):  
Joint Distribution ◽  
Survival Function ◽  
Coherent System ◽  
Series System ◽  
Survival Functions ◽  
Joint Distributions ◽  
Joint Survival Function ◽  
System Data ◽  
Incidence Functions ◽  
Set Up

In the series system (competing risks) set-up the observed data are generally accepted as the lifetime (T) and the identifier (δ) of the component causing the failure of the system. Peterson (1976) has provided bounds for the joint survival function of the component lifetimes in terms of the joint distribution of (T, δ). In the case of more complex coherent systems, there are various schemes of observation in the literature. In this paper we provide bounds for the joint and marginal survival functions of the component lifetimes in terms of the joint distribution of the data as obtained under existing and new schemes of observation. We also tackle the reverse problem of obtaining bounds for the joint distributions of the data for given marginal distributions of the component lifetimes and the distribution of the system lifetimes.

Bounds for the Joint Survival and Incidence Functions Through Coherent System Data

1997 ◽  
Vol 29 (02) ◽  
pp. 478-497
Author(s):  
J. V. Deshpande ◽  
S. R. Karia
Keyword(s):  
Joint Distribution ◽  
Survival Function ◽  
Coherent System ◽  
Series System ◽  
Survival Functions ◽  
Joint Distributions ◽  
Joint Survival Function ◽  
System Data ◽  
Incidence Functions ◽  
Set Up

In the series system (competing risks) set-up the observed data are generally accepted as the lifetime (T) and the identifier (δ) of the component causing the failure of the system. Peterson (1976) has provided bounds for the joint survival function of the component lifetimes in terms of the joint distribution of (T, δ). In the case of more complex coherent systems, there are various schemes of observation in the literature. In this paper we provide bounds for the joint and marginal survival functions of the component lifetimes in terms of the joint distribution of the data as obtained under existing and new schemes of observation. We also tackle the reverse problem of obtaining bounds for the joint distributions of the data for given marginal distributions of the component lifetimes and the distribution of the system lifetimes.

scholarly journals Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components

2013 ◽  
Vol 45 (4) ◽  
pp. 1011-1027 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Representation Theorem ◽  
Joint Distribution ◽  
Survival Function ◽  
Coherent Systems ◽  
Comparative Performance ◽  
Component Failure ◽  
Distribution Free ◽  
Joint Survival Function ◽  
Signature Vector ◽  
New Distribution

The signature of a system is defined as the vector whose ith element is the probability that the system fails concurrently with the ith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the ‘joint bivariate signature’, of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.

scholarly journals Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components

2013 ◽  
Vol 45 (04) ◽  
pp. 1011-1027 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Representation Theorem ◽  
Joint Distribution ◽  
Survival Function ◽  
Coherent Systems ◽  
Comparative Performance ◽  
Component Failure ◽  
Distribution Free ◽  
Joint Survival Function ◽  
Signature Vector ◽  
New Distribution

The signature of a system is defined as the vector whoseith element is the probability that the system fails concurrently with theith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the ‘joint bivariate signature’, of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.

scholarly journals AGING FUNCTIONS AND MULTIVARIATE NOTIONS OF NBU AND IFR

2010 ◽  
Vol 24 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Fabrizio Durante ◽  
Rachele Foschi ◽  
Fabio Spizzichino
Keyword(s):  
Failure Rate ◽  
Survival Function ◽  
Conditional Survival ◽  
Survival Functions ◽  
Increasing Failure Rate ◽  
Joint Survival Function ◽  
History Of ◽  
Aging Function ◽  
New Better Than Used ◽  
Better Than

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals.

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

Virtual clinics for follow-up of pacemakers and implantable cardioverter defibrillators in children

2019 ◽  
Vol 29 (10) ◽  
pp. 1243-1247
Author(s):  
Georgia Spentzou ◽  
Kaitlin Mayne ◽  
Helen Fulton ◽  
Karen McLeod
Keyword(s):  
Parent Satisfaction ◽  
Implantable Cardioverter Defibrillators ◽  
Cardiac Devices ◽  
Digital Medicine ◽  
Implantable Cardiac Devices ◽  
System Data ◽  
Set Up ◽  
Cardioverter Defibrillators ◽  
Virtual Clinic

AbstractThere is growing interest in the use of digital medicine to reduce the need for traditional outpatient follow-up. Remote interrogation of pacemakers and implantable cardioverter defibrillators is now possible with most devices. The aim of our study was to evaluate the safety and efficacy of virtual pacing clinics in following up children with pacemakers and implantable cardioverter defibrillators, including epicardial systems.Methods:The study was retrospective over 8 years (2010–2017), with review of patient records and analysis of downloads from the implantable cardiac devices to the virtual clinics.Results:A total of 75 patients were set up for virtual clinic follow-up during the study period, 94.5% with a pacemaker and 5.5% an implantable cardioverter defibrillator. The majority (76.8%) had an epicardial system. Data on lead impedance, battery longevity, programmed parameters, detected arrhythmias, percentage pacing and delivered defibrillator therapies were obtainable by download. Lead threshold measurements were obtainable via download in 83.7% of the devices, including epicardial systems. No concerning device issue was missed. In 15% of patients a major issue was detected remotely, including three patients with lead fractures. The virtual clinics resulted in fewer hospital attendances while enhancing monitoring and enabling more frequent device checks. The vast majority (91.4%) of families who responded to a questionnaire were satisfied with the virtual clinic follow-up.Conclusions:Virtual clinics allow safe and effective follow-up of children with pacemakers and implantable cardioverter defibrillators, including those with epicardial systems and are associated with high levels of parent satisfaction.

scholarly journals Contextuality in canonical systems of random variables

2017 ◽  
Vol 375 (2106) ◽  
pp. 20160389 ◽  
Author(s):  
Ehtibar N. Dzhafarov ◽  
Víctor H. Cervantes ◽  
Janne V. Kujala
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Canonical System ◽  
Canonical Representation ◽  
Single Pair ◽  
Canonical Systems ◽  
Joint Distributions ◽  
Content Sharing ◽  
Maximal Coupling ◽  
Quantum Revolution

Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.

APPROXIMATION OF SURVIVAL FUNCTION FOR HETEROGENEOUS POPULATIONS

2011 ◽  
Vol 162 (4) ◽  
pp. 342-358
Author(s):  
Stanisława OSTASIEWICZ
Keyword(s):  
Survival Time ◽  
Survival Function ◽  
Polish Population ◽  
Survival Functions ◽  
Heterogeneous Populations ◽  
Long Time ◽  
General Survival

For a long time demographers and actuaries have been deliberating the issue of the laws of life. A number of proposed survival functions turned out to be unsatisfactory when they were applied empirically. One of the ways to overcome the difficulties is to modify the general survival functions by introducing an additional formula characterizing the frailty of individuals. Another way is to use a mixture of appropriate distributions. In this contribution the latter approach to determine the survival time of men in the Polish population in 2009 is applied.

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