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Sequences of Improved Two-Sided Bounds for the Renewal Function and the Solutions of Renewal-Type Equations
Renewal-type and renewal equations usually do not have analytical solutions, and hence bounds for the functions satisfying such equations have a...
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Two-sided Bounds for Renewal Equations and Ruin Quantities
In this paper, the objective is to provide sequences of improved non-increasing (non-decreasing) upper (lower) bounds for the solution of (defective)...
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A Generalized Additive Hazards Model for the Analysis of Lifetime Data
The additive hazards model is often used in reliability analysis in areas like system reliability when the difference of risks under two different...
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Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes
We consider coherent and mixed systems composed of components with independent identically exponentially distributed lifetimes. We describe...
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On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components
The problem of stochastic comparison of two coherent systems has received a great attention in recent years. In the present work, we study the...
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Variability Orders
Most of the classical methods for comparing variability among distributions are based only upon summary statistics such as variance and standard...
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Some New Bounds for Moment Generating Functions of Various Life Distributions Using Mean Residual Life Functions
In this paper, we present bounds for moment generating functions of certain life distributions, including the decreasing mean residual life class. We...
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Memory of Distributions: A Renewal Theoretic Approach
Here we propose a new definition of memory of distributions in a renewal-theoretic framework and study the corresponding notions of ageing and...
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On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling
Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several...
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Introduction and Preliminaries
After giving an introduction to the area of stochastic orders, some basic definitions and notations are given in this chapter. Quantities like...
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A new discrete pareto type (IV) model: theory, properties and applications
Discrete analogue of a continuous distribution (especially in the univariate domain) is not new in the literature. The work of discretizing...
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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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On generalized orderings and ageing classes for residual life and inactivity time at random time
In this paper, we enhance the study of ageing classes and stochastic comparisons of residual life at random time (RLRT) and inactivity time at random...
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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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Distortion representations of multivariate distributions
The univariate distorted distributions were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks....
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Modelling bivariate lifetime data using copula
Generally modelling lifetime data is carried out using probability distributions with the aid of reliability functions such as hazard rate, mean...
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A residual inaccuracy measure based on the relevation transform
Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in...
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Stochastic ordering for populations of manufactured items
We develop a theory of stochastic orders for the age and the residual (remaining) lifetime for populations of manufactured identical items. The...
