General forms of Bivariate survival functions with reliability applications

2021 ◽  
pp. 43-64 ◽  
Author(s):  
Jerzy K. Filus ◽  
Lidia Z. Filus
Keyword(s):  
Survival Functions ◽  
Bivariate Survival

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

scholarly journals On Estimation of Bivariate Survival Function from Random Censored Data

2020 ◽  
pp. 422-430
Author(s):  
Rustamjon S. Muradov
Keyword(s):  
Relative Risk ◽  
Censored Data ◽  
Survival Function ◽  
Random Variables ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At present there are several approaches to estimate survival functions of vectors of lifetimes. However, some of these estimators are either inconsistent or not fully defined in the range of joint survival functions. Therefore they are not applicable in practice. In this paper three types of estimates of exponential-hazard, product-limit and relative-risk power structures for the bivariate survival function are considered when the number of summands in empirical estimates is replaced with a sequence of Poisson random variables. It is shown that proposed estimates are asymptotically equivalent. Keywords: bivariate survival function, Poisson random variables, empirical estimates

Planning the Size of Clinical Trials with Allowance for Patient Noncompliance

1990 ◽  
Vol 29 (03) ◽  
pp. 243-246 ◽  
Author(s):  
M. A. A. Moussa
Keyword(s):  
Clinical Trial ◽  
Clinical Trials ◽  
Sample Size ◽  
Event Rate ◽  
Survival Functions ◽  
Time Intervals ◽  
Patient Noncompliance ◽  
Event Rates ◽  
Larger Sample

AbstractVarious approaches are considered for adjustment of clinical trial size for patient noncompliance. Such approaches either model the effect of noncompliance through comparison of two survival distributions or two simple proportions. Models that allow for variation of noncompliance and event rates between time intervals are also considered. The approach that models the noncompliance adjustment on the basis of survival functions is conservative and hence requires larger sample size. The model to be selected for noncompliance adjustment depends upon available estimates of noncompliance and event rate patterns.

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