Approximation of mixtures of distributions

1991 ◽  
Vol 31 (2) ◽  
pp. 243-257 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Mixtures Of Distributions

Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

2021 ◽  
Vol 53 (1) ◽  
pp. 107-132
Author(s):  
Tomasz Rychlik ◽  
Fabio Spizzichino
Keyword(s):  
Order Statistics ◽  
Load Sharing ◽  
Single Component ◽  
Generalized Order Statistics ◽  
Hazard Rates ◽  
System Operation ◽  
Reliability Models ◽  
Mixtures Of Distributions ◽  
Failure Times ◽  
Generalized Order

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

The identifiability of mixtures of distributions

1969 ◽  
Vol 6 (02) ◽  
pp. 389-398 ◽  
Author(s):  
G. M. Tallis
Keyword(s):  
Distribution Function ◽  
Measurable Function ◽  
Borel Measurable Function ◽  
Mixtures Of Distributions ◽  
Image Position ◽  
Borel Measurable

This paper considers aspects of the following problem. Let F(x, θ) be a distribution function, d.f., in x for all θ and a Borel measurable function of θ. Define the mixture (Robbins (1948)), where Φ is a d.f., then it is of interest to determine conditions under which F(x) and F(x, θ) uniquely determine Φ. If there is only one Φ satisfying (1), F is said to be an identifiable mixture. Usually a consistency assumption is used whereby it is presumed that there exists at least one solution to (1).

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