PRESERVATION PROPERTIES OF A RENEWAL PROCESS STOPPED AT A RANDOM DEPENDENT TIME

2013 ◽  
Vol 27 (2) ◽  
pp. 163-175 ◽  
Author(s):  
F. G. Badía ◽  
Ji Hwan Cha
Keyword(s):  
Stochastic Process ◽  
Renewal Process ◽  
Recurrent Events ◽  
Counting Process ◽  
Stochastic Ordering ◽  
Random Time ◽  
Dependence Structure ◽  
Time Interval ◽  
Homogeneous Poisson Process ◽  
Random Time Interval

One of the interesting problems on the stochastic behavior of random recurrent events in a random time interval is to obtain the conditions under which the reliability properties of a random time T are inherited by N(T), where {N(t):t≥0} is a stochastic process. Most of the studies on the topic has been done under the assumption that the random time T and the stochastic process {N(t):t≥0} are stochastically independent. However, in practice, there can be different cases when appropriate dependence structure is more appropriate. In this paper, we study the preservation of a renewal process stopped at a random time when they are “stochastically dependent.” We discuss the stochastic ordering properties and the preservation of reliability classes for the random counting variables N(T) when the corresponding counting process is a renewal process. Furthermore, we study the preservation of NBUE (NWUE) reliability class when the counting process is a homogeneous Poisson process.

An age-dependent counting process generated from a renewal process

1988 ◽  
Vol 20 (4) ◽  
pp. 739-755 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Renewal Process ◽  
Counting Process ◽  
Intensity Function ◽  
Sufficient Condition ◽  
Minimal Repair ◽  
Homogeneous Poisson Process ◽  
Stochastic Convexity ◽  
Age Dependent ◽  
Non Homogeneous Poisson Process ◽  
Age Process

Let {N(t)} be a renewal process having the associated age process {X(t)}. Of interest is the counting process {M(t)} characterized by a non-homogeneous Poisson process with age-dependent intensity function λ (X(t)). The trivariate process {Y(t) = [M(t), N(t), X(t)]} is analyzed obtaining its Laplace transform generating function explicitly. Based on this result, asymptotic behavior of {S(t) = cM(t) + dN(t)} as t → ∞ is discussed. Furthermore, a sufficient condition is given under which {M(t), –N(t), X(t)} is stochastically monotone and associated. This condition also assures increasing stochastic convexity of {M(t)}. The usefulness of these results is demonstrated through an application to the age-dependent minimal repair problem.

Impairment of Saccadic Eye Movements by Scopolamine Treatment

1993 ◽  
Vol 76 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Giulia A. Oliva ◽  
Maria P. Bucci ◽  
Roberto Fioravanti
Keyword(s):  
Eye Movements ◽  
Intramuscular Injection ◽  
Peak Velocity ◽  
Saccadic Eye Movements ◽  
Random Time ◽  
Time Interval ◽  
Random Time Interval ◽  
Standard Deviations

The effects of Scopolamine on the dynamics of saccadic eye movements, stimulated over a random time interval, have been investigated in humans. A 0.5-mg dose of the drug (intramuscular injection) had various influences on the basic saccadic parameters. For all subjects duration increased and peak velocity decreased, while for 50% of the subjects saccades became hypometric and latency increased. Standard deviations increased consistently too. Moreover, the Scopolamine treatment affected postsaccadic fixation; at the end of many saccades, the eye drifted considerably, but stability was recovered after a few seconds.

AVERAGE NUMBER OF EVENTS AND AVERAGE REWARD

2000 ◽  
Vol 14 (4) ◽  
pp. 485-510
Author(s):  
Jie Mi
Keyword(s):  
Renewal Process ◽  
Finite Time ◽  
Counting Process ◽  
Interarrival Time ◽  
Time Interval ◽  
Average Reward ◽  
Finite Time Interval ◽  
Reward Process ◽  
The Mean ◽  
Renewal Reward Process

In a renewal process, the interarrival times are independent and identically distributed, and in a renewal reward process, the pairs of reward and interarrival time are i.i.d. Many useful results hold for these processes. This paper relaxes the assumption of identical distributions while keeping the assumption of independence. This paper explores the properties of the mean average number of occurrence of events and the mean average reward on any finite time interval. The paper also discusses the limiting properties of these two quantities and extends many results from the renewal process and renewal reward process to the more general counting process and reward sequence.

An age-dependent counting process generated from a renewal process

1988 ◽  
Vol 20 (04) ◽  
pp. 739-755 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Renewal Process ◽  
Counting Process ◽  
Intensity Function ◽  
Sufficient Condition ◽  
Minimal Repair ◽  
Homogeneous Poisson Process ◽  
Stochastic Convexity ◽  
Age Dependent ◽  
Non Homogeneous Poisson Process ◽  
Age Process

Let {N(t)} be a renewal process having the associated age process {X(t)}. Of interest is the counting process {M(t)} characterized by a non-homogeneous Poisson process with age-dependent intensity function λ (X(t)). The trivariate process {Y(t) = [M(t), N(t), X(t)]} is analyzed obtaining its Laplace transform generating function explicitly. Based on this result, asymptotic behavior of {S(t) = cM(t) + dN(t)} as t → ∞ is discussed. Furthermore, a sufficient condition is given under which {M(t), –N(t), X(t)} is stochastically monotone and associated. This condition also assures increasing stochastic convexity of {M(t)}. The usefulness of these results is demonstrated through an application to the age-dependent minimal repair problem.

Skunks and gray foxes in a tropical dry region: casual or positive interactions?

Mammalia ◽  
2020 ◽  
Vol 84 (5) ◽  
pp. 469-474
Author(s):  
Gabriela Pérez-Irineo ◽  
Salvador Mandujano ◽  
Eva López-Tello
Keyword(s):  
Biosphere Reserve ◽  
Camera Traps ◽  
Random Time ◽  
Positive Interactions ◽  
Time Interval ◽  
Urocyon Cinereoargenteus ◽  
Random Time Interval ◽  
Overlap Coefficient ◽  
Total Effort ◽  
Negative Interactions

AbstractPrevious studies have shown that skunks present negative interactions with foxes. However, recently published observations have demonstrated that southern spotted skunk (Spilogale angustifrons) individuals follow gray foxes (Urocyon cinereoargenteus) in the Tehuacán-Cuicatlán Biosphere Reserve (TCBR) in Mexico. In this paper, we reported the same interaction in other locations in the TCBR and evaluated whether this interaction is casual or statistically positive. In this analysis, we included data pertaining to three skunk species (S. angustifrons, Conepatus leuconotus, and Mephitis macroura) and U. cinereoargenteus. We sampled 172 sites using camera traps from 2011 to 2018 for a total effort of 49,764 trap-days. The four studied species were nocturnal; the overlap coefficient between foxes and skunks varied from 0.70 to 0.83. Of the 32 consecutive records between S. angustifrons and U. cinereoargenteus, 11 showed that individuals of this skunk species closely followed U. cinereoargenteus and that these encounters were not random (time interval <1 min). We did not find evidence of a behavioral association of U. cinereoargenteus with C. leuconotus and M. macroura.

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