Age and residual lifetime distributions for branching processes

2007 ◽  
Vol 77 (5) ◽  
pp. 503-513 ◽  
Author(s):  
A. Yakovlev ◽  
N. Yanev
Keyword(s):  
Branching Processes ◽  
Residual Lifetime ◽  
Lifetime Distributions

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.

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.

A GENERALIZED ENTROPY-BASED RESIDUAL LIFETIME DISTRIBUTIONS

2011 ◽  
Vol 04 (02) ◽  
pp. 171-184 ◽  
Author(s):  
VIKAS KUMAR ◽  
H. C. TANEJA
Keyword(s):  
Residual Life ◽  
Survival Function ◽  
Monotonicity Property ◽  
Entropy Measure ◽  
Residual Lifetime ◽  
Mean Residual Life ◽  
Present Communication ◽  
Dynamic Information ◽  
Lifetime Distributions ◽  
Life Function

The present communication considers Havrda and Charvat entropy measure to propose a generalized dynamic information measure. It is shown that the proposed measure determines the survival function uniquely. The residual lifetime distributions have been characterized. A bound for the dynamic entropy measure in terms of mean residual life function has been derived, and its monotonicity property is studied.

ON SOME PROPERTIES OF A CLASS OF MULTIVARIATE ERLANG MIXTURES WITH INSURANCE APPLICATIONS

2014 ◽  
Vol 45 (1) ◽  
pp. 151-173 ◽  
Author(s):  
Gordon E. Willmot ◽  
Jae-Kyung Woo
Keyword(s):  
Residual Lifetime ◽  
Risk Allocation ◽  
Insurance Risk ◽  
Lifetime Distributions ◽  
Scale Parameters ◽  
Distributional Properties ◽  
Premium Calculation ◽  
Equilibrium Distributions ◽  
Stop Loss ◽  
Erlang Distributions

AbstractWe discuss some properties of a class of multivariate mixed Erlang distributions with different scale parameters and describes various distributional properties related to applications in insurance risk theory. Some representations involving scale mixtures, generalized Esscher transformations, higher-order equilibrium distributions, and residual lifetime distributions are derived. These results allows for the study of stop-loss moments, premium calculation, and the risk allocation problem. Finally, some results concerning minimum and maximum variables are derived and applied to pricing joint life and last survivor policies.

scholarly journals Some new results on bathtub-shaped hazard rate models

2021 ◽  
Vol 19 (2) ◽  
pp. 1239-1250
Author(s):  
Mohamed Kayid ◽  
Keyword(s):  
Order Statistics ◽  
Hazard Rate ◽  
Residual Life ◽  
Change Points ◽  
Residual Lifetime ◽  
Lifetime Distributions ◽  
Residual Life Function ◽  
Basic Model ◽  
Quantile Residual Life ◽  
Life Function

<abstract><p>The most common non-monotonic hazard rate situations in life sciences and engineering involves bathtub shapes. This paper focuses on the quantile residual life function in the class of lifetime distributions that have bathtub-shaped hazard rate functions. For this class of distributions, the shape of the $ \alpha $-quantile residual lifetime function was studied. Then, the change points of the $ \alpha $-quantile residual life function of a general weighted hazard rate model were compared with the corresponding change points of the basic model in terms of their location. As a special weighted model, the order statistics were considered and the change points related to the order statistics were compared with the change points of the baseline distribution. Moreover, some comparisons of the change points of two different order statistics were presented.</p></abstract>

Applications of the age distribution in age dependent branching processes

1966 ◽  
Vol 3 (1) ◽  
pp. 179-201 ◽  
Author(s):  
Howard J. Weiner
Keyword(s):  
Markov Process ◽  
Markov Models ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Age Distribution ◽  
Lifetime Distributions ◽  
Age Dependent ◽  
Semi Markov Process ◽  
Model Section ◽  
Number Of Cells

This paper considers asymptotic properties of increasing population age dependent branching processes which have a limiting age distribution. In Section I, the Bellman-Harris model [2] is altered in accord with a suggestion by Kendall [3]. The effect of this modification on the applicable results of [3] is indicated. An extension to the case where each cell passes through a sequence of states to mitosis or proceeds from state to state in accord with a semi-Markov process to mitosis is considered. Section 1.1 considers asymptotic moments for the total number of cells. Section 1.2 treats moments in a sequence-of-states model [4]. Section 1.3 extends the results of 1.2 to a semi-Markov model. Section 1.4 treats various asymptotic lifetime distributions and fraction of cells in a given state for both the sequence-of-states and semi-Markov models.

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