Characterizations of Lifetime Distributions Based on Doubly Truncated Mean Residual Life and Mean Past to Failure

Khorashadizadeh, Mohammad; Roknabadi, A. H. Rezaei; Borzadaran, Gholam Reza Mohtashami

doi:10.1080/03610926.2010.535626

Cited by 15 publications

(9 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, through such modified models, it may be possible to determine the existence (or non-existence) of Hopf bifurcations by examining whether

is periodic, as this seems like it would be a requirement for such behavior in reality. Additional avenues for investigation include the direct extension to periodic compartmental models ( Wang & Zhao, 2008 ) through the use of some form of double truncated mean residual waiting-time ( Khorashadizadeh et al., 2012 ), and a thorough comparison to renewal equations ( Champredon et al., 2018 ), as such work would likely prove valuable for the study infectious disease dynamics.…”

Section: Discussionmentioning

confidence: 99%

A generalized differential equation compartmental model of infectious disease transmission

Greenhalgh

Rozins

2021

Infectious Disease Modelling

View full text Add to dashboard Cite

For decades, mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression, control, and prevention of disease spread. Of these models, one of the most fundamental is the SIR differential equation model. However, this ubiquitous model has one significant and rarely acknowledged shortcoming: it is unable to account for a disease's true infectious period distribution. As the misspecification of such a biological characteristic is known to significantly affect model behavior, there is a need to develop new modeling approaches that capture such information. Therefore, we illustrate an innovative take on compartmental models, derived from their general formulation as systems of nonlinear Volterra integral equations, to capture a broader range of infectious period distributions, yet maintain the desirable formulation as systems of differential equations. Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations, instead of the typical inflated model sizes required by traditional differential equation compartmental models, and a compartmental model that captures any mean, standard deviation, skewness, and kurtosis of an infectious period distribution with 4 differential equations. The significance of our work is that it opens up a new class of easy-to-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory, and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics, public health, and evolutionary biology.

show abstract

“…In addition, through such modified models, it may be possible to determine the existence (or non-existence) of Hopf bifurcations by examining whether

Section: Discussionmentioning

confidence: 99%

A generalized differential equation compartmental model of infectious disease transmission

Greenhalgh

Rozins

2021

Infectious Disease Modelling

View full text Add to dashboard Cite

show abstract

“…We remark that the ≤ LUI -order is analogous to the ≤ LU -order, which was introduced by Ebrahimi ad Pellerey in [36] in order to compare the information contents in random lifetimes and to perform classification of systems. Hence, recalling the interval entropy (20), Definition 3 expresses that, given two systems that are both failed in the interval [u, t], the condition H X (u, t) ≤ H Y (u, t) expresses that the uncertainty about the predictability of the failure time occurred in the interval [u, t] for the first system is less than that for the second one in the same interval.…”

Section: Remarkmentioning

confidence: 99%

“…Sankaran and Sunoj [12]) and of the conditional expectations (see Su and Huang [13], Ahmad [14], Betensky and Martin [15], Navarro and Ruiz [16], Bairamov and Gebizlioglu [17], Poursaeed and Nematollahi [18], and Sunoj et al [19]). We also recall the analysis of the doubly truncated mean residual lifetime and the doubly truncated mean past to failure performed by Khorashadizadeh et al [20].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

2020

View full text Add to dashboard Cite

A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x ∈ ( u , t ) , which is finalized to measure the goodness of the replacement procedure. The characterization and the properties of the differential entropy of the system lifetime are also discussed. Finally, an example of application to the firing activity of a stochastic neuronal model is provided.

show abstract

“…Such a random variable can be called reversed residual lifetime, or the time elapsed after failure till time a , given that the unit has already failed by time a . In such situations, this random variable was found to be more adequate than the residual random variable ( [10] and [19]). This paved the way of studying many reliability concepts in the reversed time scale.…”

Section: Definitions and Notionsmentioning

confidence: 99%

“…The reversed residual lifetime random variable was introduced by many researchers recently (c.f. [1], [4], [5], [10], [11], [13], [14]).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic properties of discrete mean and variance reversed residual lifetime functions

Mahdy¹

2013

ams

View full text Add to dashboard Cite

show abstract

Characterizations of Lifetime Distributions Based on Doubly Truncated Mean Residual Life and Mean Past to Failure

Cited by 15 publications

References 17 publications

A generalized differential equation compartmental model of infectious disease transmission

A generalized differential equation compartmental model of infectious disease transmission

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

Probabilistic properties of discrete mean and variance reversed residual lifetime functions

Contact Info

Product

Resources

About