On non-monotonic ageing properties from the Laplace transform, with actuarial applications

Belzunce, Félix; Ortega, Eva; Ruiz, J.

doi:10.1016/j.insmatheco.2006.01.010

Cited by 39 publications

(23 citation statements)

References 33 publications

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“…We shall prove the analogus result for the IDMRL class of life distributions. To prove the theorem, we shall need a result which is proved in Belzunce et al (2007) using total positivity theory. For completeness, we give the result in Lemma 3.1 below.…”

Section: Poisson Shock Models Leading To Idmrl Distributionsmentioning

confidence: 99%

On some properties of the IDMRL class of life distributions

Anis

2012

Journal of Statistical Planning and Inference

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Section: Poisson Shock Models Leading To Idmrl Distributionsmentioning

confidence: 99%

On some properties of the IDMRL class of life distributions

Anis

2012

Journal of Statistical Planning and Inference

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“…The potential complexity of the difference is illustrated by 'simple' examples in Table 1. Despite the complex relationship between the original and new MRL functions, Belzunce, Ortega & Ruiz (2007) show that if the MRL function µ(t) is UBT, then its turning point τ * is smaller then the turning point τ * λ of µ λ (t), for every λ > 0. From this, using Theorem 3, we infer several facts.…”

Section: Interactions Between Hazard Rate and Mean Residual Life Funcmentioning

confidence: 93%

Bathtub‐type Curves in Reliability and Beyond

Lai¹,

Zitikis

2007

Aus NZ J of Statistics

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Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub-type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.

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“…Assuming that the insurer provides a payment of one monetary unit after death, then the net prospective premium reserve V X ( t ; δ , β ) is given by (see the book of Rolski et al31(p352))

V_{X} (t; δ, β) = E [e^{- δ (X - t)} | X > t] - β E [\int_{0}^{X - t} e^{- δ x} d x| X > t],

where δ > 0 is the force of interest and β > 0 is the constant premium rate. Integrating by parts, we have (see the work of Belzunce et al)

V_{X} false(t; δ, β false) = 1 - false(δ + β false) {\overset{a}{true}}_{X} false(t; δ false),

where

{\overset{a}{true}}_{X} false(t; δ false)

is defined in . Similarly, let V Y ( t ; δ , β ) denote the net prospective premium reserve of the lifetime Y , so that

V_{X} (t; δ, β) - V_{Y} (t; δ, β) = (δ + β) [{\overset{true‾}{a}}_{Y} (t; δ) - {\overset{true‾}{a}}_{X} (t; δ)] .

Hence, by applying Proposition , we have that the difference between the net prospective premium reserves of the considered life...…”

Section: Additive Hazard Modelmentioning

confidence: 99%

Probabilistic mean value theorems for conditioned random variables with applications

Crescenzo

Psarrakos

2019

Appl Stoch Models Bus & Ind

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In this paper, we propose a probabilistic analogue of the mean value theorem for conditional nonnegative random variables ordered in the hazard rate and reversed hazard rate order, upon conditioning on intervals of the form (t,∞) and [0,t]. This result is then specialized within the proportional hazards model and the proportional reversed hazards model with applications to series systems in reliability theory and to absorption random times of linear birth‐death processes. We also study the comparison of residual entropies and discuss some connections to Wasserstein and stop‐loss distances of random variables. A treatment for the additive hazard rate model is finally provided, with an application to life annuities.

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On non-monotonic ageing properties from the Laplace transform, with actuarial applications

Cited by 39 publications

References 33 publications

On some properties of the IDMRL class of life distributions

On some properties of the IDMRL class of life distributions

Bathtub‐type Curves in Reliability and Beyond

Probabilistic mean value theorems for conditioned random variables with applications

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