scholarly journals The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2831
Author(s):  
Vladimir Rusev ◽  
Alexander Skorikov
Keyword(s):  
Asymptotic Behavior ◽  
Exponential Distribution ◽  
Wide Class ◽  
Heavy Tails ◽  
Domain Of Attraction ◽  
Reliability Theory ◽  
Residual Lifetime ◽  
Long Time

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.

Characterizing the Exponential Law Under Laplace Order Domination

1995 ◽  
Vol 45 (3-4) ◽  
pp. 171-178 ◽  
Author(s):  
Murari Mitra ◽  
Sujit K. Basu ◽  
M. C. Bhattacharjee
Keyword(s):  
Exponential Distribution ◽  
Reliability Theory ◽  
Subject Classification ◽  
Exponential Law ◽  
Life Distributions

Interesting characterizations of the exponential distribution have been obtained in classes of life distributions important in reliability theory. The results strengthen some of the analogous conclusions already existing in the literature. AMS (1991) Subject Classification No. Primary 62NOS: Secondaey 90825. 60F99.

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

scholarly journals Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Moez Benhamed ◽  
Sahar Mohammad Abusalim
Keyword(s):  
Asymptotic Behavior ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time

In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that θtX1−2α vanishes at infinity.

Asymptotic behavior of Hill's estimate and applications

1986 ◽  
Vol 23 (04) ◽  
pp. 922-936
Author(s):  
Gane Samb Lo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Finite Number ◽  
Domain Of Attraction ◽  
Distribution Functions ◽  
Complete Theory ◽  
General Distribution ◽  
Stable Law ◽  
Biological Phenomena ◽  
Pareto’S Law

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.

Sign in / Sign up

Export Citation Format

Share Document