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

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1203 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Patrizia Di Gironimo ◽  
Suchandan Kayal
Keyword(s):  
Random Variable ◽  
Fixed Time ◽  
Neuronal Model ◽  
Lifetime Distribution ◽  
Differential Entropy ◽  
Firing Activity ◽  
Stochastic Comparisons ◽  
The Past ◽  
Replacement Procedure ◽  
Replacement Model

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.

scholarly journals Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 204 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Patrizia Di Gironimo
Keyword(s):  
Fixed Time ◽  
Lifetime Distribution ◽  
Differential Entropy ◽  
Stochastic Comparisons ◽  
Dynamic Information ◽  
Relative Ratio ◽  
Replacement Procedure ◽  
Replacement Model ◽  
Suitable Index

We consider a suitable replacement model for random lifetimes, in which at a fixed time an item is replaced by another one having the same age but different lifetime distribution. We focus first on stochastic comparisons between the involved random lifetimes, in order to assess conditions leading to an improvement of the system. Attention is also given to the relative ratio of improvement, which is proposed as a suitable index finalized to measure the goodness of the replacement procedure. Finally, we provide various results on the dynamic differential entropy of the lifetime of the improved system.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Mixture copulas and insurance applications

2018 ◽  
Vol 12 (2) ◽  
pp. 391-411
Author(s):  
Maissa Tamraz
Keyword(s):  
Joint Distribution ◽  
Stable Distribution ◽  
Random Variable ◽  
Fixed Time ◽  
Collective Model ◽  
Data Sets ◽  
New Model ◽  
Time Period ◽  
Insurance Data ◽  
Dependence Property

AbstractIn the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distributionFof the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variableNfollows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property ofFwith respect to both parametersαandλ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

An Agent-Based Model of Lost Person Dynamics for Enabling Wilderness Search and Rescue

2019 ◽  
Author(s):  
Amanda Hashimoto ◽  
Nicole Abaid
Keyword(s):  
Real World ◽  
Random Variable ◽  
Fixed Time ◽  
Search And Rescue ◽  
Agent Based Model ◽  
Real World Data ◽  
Agent Based ◽  
World Data ◽  
Analogous Data ◽  
Behavior Strategies

Abstract In this paper, we introduce an agent-based model of lost person behavior that may be used to improve current methods for wilderness search and rescue (SAR). The model defines agents moving on a landscape with behavior considered as a random variable. The behavior uses a distribution of four known lost person behavior strategies in order to simulate possible trajectories for the agent. We simulate all possible distributions of behaviors in the model and compute distributions of horizontal distances traveled in a fixed time. By comparing these results to analogous data from a database of lost person cases, we explore the model’s validity with respect to real-world data.

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 An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations

2020 ◽  
Vol 5 (1) ◽  
pp. 337-348 ◽  
Author(s):  
Nihal İnce ◽  
Aladdin Shamilov
Keyword(s):  
Probability Density Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Density Function ◽  
Model Fitting ◽  
Random Variable ◽  
Optimization Methods ◽  
Fixed Time ◽  
New Method

AbstractIn this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.

PRESERVATION OF LOG-CONCAVITY AND LOG-CONVEXITY UNDER OPERATORS

2020 ◽  
pp. 1-14
Author(s):  
Wanwan Xia ◽  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Distribution Function ◽  
Operations Research ◽  
Random Variable ◽  
Group Property ◽  
Semi Group ◽  
Real Numbers ◽  
Bernstein Type ◽  
Stochastic Comparisons ◽  
Weighted Distributions ◽  
The Family

Log-concavity [log-convexity] and their various properties play an increasingly important role in probability, statistics, operations research and other fields. In this paper, we first establish general preservation theorems of log-concavity and log-convexity under operator $\phi \longmapsto T(\phi , \theta )=\mathbb {E}[\phi (X_\theta )]$ , θ ∈ Θ, where Θ is an interval of real numbers or an interval of integers, and the random variable $X_\theta$ has a distribution function belonging to the family $\{F_\theta , \theta \in \Theta \}$ possessing the semi-group property. The proofs are based on the theory of stochastic comparisons and weighted distributions. The main results are applied to some special operators, for example, operators occurring in reliability, Bernstein-type operators and Beta-type operators. Several known results in the literature are recovered.

Stochastic comparisons of random minima and maxima

1997 ◽  
Vol 34 (02) ◽  
pp. 420-425 ◽  
Author(s):  
Moshe Shaked ◽  
Tityik Wong
Keyword(s):  
Positive Integer ◽  
Random Variables ◽  
Random Variable ◽  
Independent Random Variables ◽  
Stochastic Comparison ◽  
Stochastic Comparisons ◽  
Comparison Results

Let X 1, X 2,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the Xi. In this paper we obtain some stochastic comparison results involving min {X 1, X 2,…, XN ) and max{X 1, X 2,…, XN }.

An age dependent branching process with variable lifetime distribution: The generation size

1974 ◽  
Vol 6 (02) ◽  
pp. 291-308 ◽  
Author(s):  
Robert Fildes
Keyword(s):  
Branching Process ◽  
Random Variable ◽  
Lifetime Distribution ◽  
Mean Square ◽  
Initial Particle ◽  
Age Dependent ◽  
The Mean ◽  
Watson Process ◽  
Number Of Particles

In a branching process with variable lifetime, introduced by Fildes (1972) define Yjk (t) as the number of particles alive in generation k at time t when the initial particle is born in generation j. A limit law similar to that derived in the Bellman-Harris process is proved where it is shown that Yjk (t) suitably normalised converges in mean square to a random variable which is the limit random variable of Znm–n in the Galton-Watson process (m is the mean number of particles born).

A note on stochastic ordering of order statistics

1997 ◽  
Vol 34 (03) ◽  
pp. 785-789 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Order Statistics ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stochastic Comparisons ◽  
Homogeneous Population ◽  
Independent Components ◽  
Binomial Random Variable ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial random variable. It is then used to deal with the stochastic comparisons of order statistics from heterogeneous populations with those from a homogeneous population. The result has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.

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