scholarly journals On preservation of some partial orderings under shock models

1990 ◽  
Vol 22 (02) ◽  
pp. 508-509 ◽  
Author(s):  
Subhash C. Kochar
Keyword(s):  
Poisson Process ◽  
Homogeneous Poisson Process ◽  
Shock Models ◽  
Partial Orderings ◽  
Life Distributions

Singh and Jain (1989) have proved some preservation results for partial orderings of life distributions assuming that shocks occur according to a homogeneous Poisson process. It is shown that their results hold under less restrictive conditions.

scholarly journals On preservation of some partial orderings under shock models

1990 ◽  
Vol 22 (2) ◽  
pp. 508-509 ◽  
Author(s):  
Subhash C. Kochar
Keyword(s):  
Poisson Process ◽  
Homogeneous Poisson Process ◽  
Shock Models ◽  
Partial Orderings ◽  
Life Distributions

Singh and Jain (1989) have proved some preservation results for partial orderings of life distributions assuming that shocks occur according to a homogeneous Poisson process. It is shown that their results hold under less restrictive conditions.

Preservation of certain classes of life distributions under Poisson shock models

1994 ◽  
Vol 31 (2) ◽  
pp. 458-465 ◽  
Author(s):  
Enrico Fagiuoli ◽  
Franco Pellerey
Keyword(s):  
Poisson Process ◽  
Sufficient Conditions ◽  
Life Distribution ◽  
Shock Models ◽  
Life Distributions

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

Preservation of certain classes of life distributions under Poisson shock models

1994 ◽  
Vol 31 (02) ◽  
pp. 458-465 ◽  
Author(s):  
Enrico Fagiuoli ◽  
Franco Pellerey
Keyword(s):  
Poisson Process ◽  
Sufficient Conditions ◽  
Life Distribution ◽  
Shock Models ◽  
Life Distributions

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (03) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (3) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽  
2013 ◽  
Vol 34 (6) ◽  
pp. 434-437 ◽  
Author(s):  
Donald W. MacKenzie
Keyword(s):  
Poisson Process ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Massachusetts Institute Of Technology ◽  
Homogeneous Poisson Process ◽  
Cornell University ◽  
The Difference ◽  
Suicide Clusters ◽  
Institute Of Technology ◽  
Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

scholarly journals The fighter problem: optimal allocation of a discrete commodity

2011 ◽  
Vol 43 (01) ◽  
pp. 121-130 ◽  
Author(s):  
Jay Bartroff ◽  
Ester Samuel-Cahn
Keyword(s):  
Poisson Process ◽  
Optimal Allocation ◽  
Optimal Number ◽  
Homogeneous Poisson Process ◽  
Time Period

In this paper we study the fighter problem with discrete ammunition. An aircraft (fighter) equipped with n anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If j of the n missiles are spent at an encounter, they destroy an enemy plane with probability a(j), where a(0) = 0 and {a(j)} is a known, strictly increasing concave sequence, e.g. a(j) = 1 - q j , 0 < q < 1. If the enemy is not destroyed, the enemy shoots the fighter down with known probability 1 - u, where 0 ≤ u ≤ 1. The goal of the fighter is to shoot down as many enemy airplanes as possible during a given time period [0, T]. Let K(n, t) be the smallest optimal number of missiles to be used at a present encounter, when the fighter has flying time t remaining and n missiles remaining. Three seemingly obvious properties of K(n, t) have been conjectured: (A) the closer to the destination, the more of the n missiles one should use; (B) the more missiles one has; the more one should use; and (C) the more missiles one has, the more one should save for possible future encounters. We show that (C) holds for all 0 ≤ u ≤ 1, that (A) and (B) hold for the ‘invincible fighter’ (u = 1), and that (A) holds but (B) fails for the ‘frail fighter’ (u = 0); the latter is shown through a surprising counterexample, which is also valid for small u > 0 values.

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