scholarly journals The Complementary Exponentiated Exponential Geometric Lifetime Distribution

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Francisco Louzada ◽  
Vitor Marchi ◽  
James Carpenter
Keyword(s):  
Practical Importance ◽  
Formal Proof ◽  
Residual Lifetime ◽  
Lifetime Distributions ◽  
Hazard Functions ◽  
New Family ◽  
Maximum Likelihood Procedure ◽  
Mean Residual Lifetime ◽  
Risk Scenario ◽  
Modified Weibull

We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments,rth moment of theith order statistic, mean residual lifetime, and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.

scholarly journals A Dynamic Failure Time Degradation-Based Model

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1532
Author(s):  
Abdulhakim A. Albabtain ◽  
Mansour Shrahili ◽  
Lolwa Alshagrawi ◽  
Mohamed Kayid
Keyword(s):  
Hazard Rate ◽  
Failure Time ◽  
Degradation Process ◽  
Residual Lifetime ◽  
Time To Failure ◽  
Lifetime Distributions ◽  
Mean Residual Lifetime ◽  
Aging Properties ◽  
Degradation Models ◽  
Characterization Property

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.

ON CLASSES OF LIFETIME DISTRIBUTIONS WITH UNKNOWN AGE

2000 ◽  
Vol 14 (4) ◽  
pp. 473-484 ◽  
Author(s):  
Gordon E. Willmot ◽  
Jun Cai
Keyword(s):  
Queueing Theory ◽  
Residual Lifetime ◽  
Lifetime Distributions ◽  
Poisson Distributions ◽  
Mean Residual Lifetime ◽  
Aging Properties ◽  
Life Distributions

Some class properties of the used better (worse) than aged [UBA (UWA)] and the used better (worse) than aged in expectation [UBAE (UWAE)] classes of lifetime distributions are considered. Relationships with the decreasing (increasing) mean residual lifetime [DMRL (IMRL)] class and the decreasing (increasing) variance residual lifetime [DVRL (IVRL)] class are established. Discrete UBA and UWA distributions are introduced and studied. Characterizations of UBA and UWA distributions are derived by using discrete aging properties of mixed Poisson distributions. Applications of these results to queueing theory and ruin are then considered. In particular, preservation of UBA (UWA) and UBAE (UWAE) under a transform of life distributions is given.

scholarly journals On estimating optimal regime for treatment initiation time based on restricted mean residual lifetime

Biometrics ◽  
2021 ◽  
Author(s):  
Xin Chen ◽  
Rui Song ◽  
Jiajia Zhang ◽  
Swann Arp Adams ◽  
Liuquan Sun ◽  
...  
Keyword(s):  
Treatment Initiation ◽  
Residual Lifetime ◽  
Initiation Time ◽  
Optimal Regime ◽  
Mean Residual Lifetime

Entropy-based measure of uncertainty in past lifetime distributions

2002 ◽  
Vol 39 (02) ◽  
pp. 434-440 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Maria Longobardi
Keyword(s):  
Shannon Entropy ◽  
Lifetime Distribution ◽  
Residual Entropy ◽  
Residual Lifetime ◽  
Lifetime Distributions ◽  
The Past ◽  
Life Distributions ◽  
Measure Of Uncertainty

As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

scholarly journals On the nonoptimality of the foreground-background discipline for IMRL service times

2006 ◽  
Vol 43 (02) ◽  
pp. 523-534
Author(s):  
S. Aalto ◽  
U. Ayesta
Keyword(s):  
Hazard Rate ◽  
Residual Lifetime ◽  
Processor Sharing ◽  
Counter Example ◽  
Mean Delay ◽  
Mean Residual Lifetime ◽  
Service Disciplines ◽  
The Mean ◽  
Service Times ◽  
The One

It is known that for decreasing hazard rate (DHR) service times the foreground-background discipline (FB) minimizes the mean delay in the M/G/1 queue among all work-conserving and nonanticipating service disciplines. It is believed that a similar result is valid for increasing mean residual lifetime (IMRL) service times. However, on the one hand, we point out a flaw in an earlier proof of the latter result and construct a counter-example that demonstrates that FB is not necessarily optimal within class IMRL. On the other hand, we prove that the mean delay for FB is smaller than that of the processor-sharing discipline within class IMRL, giving a weaker version of an earlier hypothesis.

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