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Exact Results and Bounds for the Joint Tail and Moments of the Recurrence Times in a Renewal Process
The best known result about the joint distribution of the backward and forward recurrence times in a renewal process concerns the asymptotic behavior...
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Stochastic Precedence and Minima Among Dependent Variables
The notion of stochastic precedence between two random variables emerges as a relevant concept in several fields of applied probability. When one...
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Gamma Process-Based Models for Disease Progression
Classic chronic diseases progression models are built by gauging the movement from the disease free state, to the preclinical (asymptomatic) one, in...
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Limit distributions of the upper order statistics for the Lévy-frailty Marshall-Olkin distribution
The Marshall-Olkin (MO) distribution is considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of...
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Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models
In actuarial science, it is often of interest to compare stochastically extreme claim amounts from heterogeneous portfolios. In this regard, in the...
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Moments of the Forward Recurrence Time in a Renewal Process
The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability...
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Stochastic comparisons of series systems with independent heterogeneous Lomax-exponential components
Due to the flexibility of the hazard rate function of the Lomaxexponential distribution, it provides a good alternative for some existing life...
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SIR-Type Epidemic Models as Block-Structured Markov Processes
This paper proposes a block-structured Markov process to describe the spread of epidemics of Susceptible-Infected-Removed (SIR) type. Our purpose is...
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Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems
The main object of this research is a functional limit theorem under conditions of heavy traffic in multi-phase queueing systems. In this paper,...
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Fluctuation Analysis in Parallel Queues with Hysteretic Control
We study an enhanced hysteretic control system, with primary and secondary queues and random batch service. When the primary queue down-crosses r ,...
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Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model
In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the...
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Extensions of the Generalized Pólya Process
A new self-exciting counting process is here considered, which extends the generalized Pólya process introduced by Cha (Adv Appl Probab 46:1148–1171,
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Sharp Bounds for Exponential Approximations of NWUE Distributions
Let F be an NWUE distribution with mean 1 and G be the stationary renewal distribution of F . We would expect G to converge in distribution to the...
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Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model
In this paper, we focus on analyzing the relationship between the discounted aggregate claim costs until ruin and ruin-related quantities including...
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On a New Shot Noise Process and the Induced Survival Model
Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock...
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The Distribution of a Sum of Independent Binomial Random Variables
The distribution of a sum S of independent binomial random variables, each with different success probabilities, is discussed. An efficient algorithm...
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Risk Diversifying Treaty Between Two Companies with Only One in Insurance Business
We consider an insurance company (Company 1) and another company (Company 2) operating under a risk diversification treaty; we assume that Company 2...
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Approximate Simulation Techniques and Distribution of an Extended Gamma Process
In reliability theory, many papers use a standard Gamma process to model the evolution of the cumulative deterioration of a system over time. When...
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Laplace transform ordering of time to failure in age replacement models
The concept of mean time to failure in age replacement models plays an important role in reliability and life testing. In this paper, based on the...
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Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times
The system’s performance is one of most important issues in both theory and practice. The task of evaluation of system performance first needs a...