Some properties of ageing notions based on the moment-generating-function order

2004 ◽  
Vol 41 (3) ◽  
pp. 927-934 ◽  
Author(s):  
Xiaohu Li
Keyword(s):  
Generating Function ◽  
Renewal Process ◽  
Moment Generating Function ◽  
Stochastic Comparison ◽  
Life Distributions ◽  
Convex Linear Combination ◽  
The Moment ◽  
New Better Than Used ◽  
Ageing Notions ◽  
Better Than

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class ℳ is closed under both convex linear combination and geometric compounding. Secondly, the class NBUmg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBUmg interarrivals is studied.

Some properties of ageing notions based on the moment-generating-function order

2004 ◽  
Vol 41 (03) ◽  
pp. 927-934 ◽  
Author(s):  
Xiaohu Li
Keyword(s):  
Generating Function ◽  
Renewal Process ◽  
Moment Generating Function ◽  
Stochastic Comparison ◽  
Life Distributions ◽  
Convex Linear Combination ◽  
The Moment ◽  
New Better Than Used ◽  
Ageing Notions ◽  
Better Than

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class ℳ is closed under both convex linear combination and geometric compounding. Secondly, the class NBUmg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBUmg interarrivals is studied.

scholarly journals Some New Results on the Moment Generating Function Order and Related Life Distributions

2010 ◽  
Vol 47 (04) ◽  
pp. 923-933
Author(s):  
Shuhong Zhang ◽  
Xiaohu Li
Keyword(s):  
Generating Function ◽  
Moment Generating Function ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Stochastic Comparisons ◽  
Life Distributions ◽  
The Moment ◽  
Age Replacement ◽  
New Better Than Used ◽  
Better Than

In this paper we study the moment generating function order and the new better than used in the moment generating function order (NBUMG) life distributions. A closure property of this order under an independent random sum is deduced, and stochastic comparisons among the block replacement policy, the age replacement policy, the complete repair policy, and the minimal repair policy of an NBUMG component are investigated.

scholarly journals Some New Results on the Moment Generating Function Order and Related Life Distributions

2010 ◽  
Vol 47 (4) ◽  
pp. 923-933 ◽  
Author(s):  
Shuhong Zhang ◽  
Xiaohu Li
Keyword(s):  
Generating Function ◽  
Moment Generating Function ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Stochastic Comparisons ◽  
Life Distributions ◽  
The Moment ◽  
Age Replacement ◽  
New Better Than Used ◽  
Better Than

In this paper we study the moment generating function order and the new better than used in the moment generating function order (NBUMG) life distributions. A closure property of this order under an independent random sum is deduced, and stochastic comparisons among the block replacement policy, the age replacement policy, the complete repair policy, and the minimal repair policy of an NBUMG component are investigated.

On an ageing class based on the moment generating function order

2018 ◽  
Vol 55 (2) ◽  
pp. 402-415 ◽  
Author(s):  
Shyamal Ghosh ◽  
Murari Mitra
Keyword(s):  
Weak Convergence ◽  
Generating Function ◽  
Model Theory ◽  
Damage Model ◽  
Moment Generating Function ◽  
Shock Model ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Moment ◽  
Moment Bounds

Abstract We develop shock model theory in different scenarios for the ℳ-class of life distributions introduced by Klar and Müller (2003). We also study the cumulative damage model of A-Hameed and Proschan (1975) in the context of ℳ-class and establish analogous results. We obtain moment bounds and explore weak convergence issues within the ℳ-class of life distributions.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

Problèmes de premier passage résolubles par la méthode de séparation des variables

1995 ◽  
Vol 32 (02) ◽  
pp. 337-348
Author(s):  
Mario Lefebvre
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Generating Function ◽  
Moment Generating Function ◽  
First Passage Times ◽  
Standard Brownian Motion ◽  
First Passage ◽  
The Moment ◽  
Passage Times

In this paper, bidimensional stochastic processes defined by ax(t) = y(t)dt and dy(t) = m(y)dt + [2v(y)]1/2 dW(t), where W(t) is a standard Brownian motion, are considered. In the first section, results are obtained that allow us to characterize the moment-generating function of first-passage times for processes of this type. In Sections 2 and 5, functions are computed, first by fixing the values of the infinitesimal parameters m(y) and v(y) then by the boundary of the stopping region.

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