The minimum of a stationary Markov process superimposed on a U-shaped trend

1969 ◽  
Vol 6 (02) ◽  
pp. 399-408 ◽  
Author(s):  
H.E. Daniels
Keyword(s):  
Markov Process ◽  
Stationary Process ◽  
Probability Distributions ◽  
Asymptotic Independence ◽  
Curved Boundary ◽  
Sample Paths ◽  
Winter Temperatures ◽  
Free Case ◽  
Stationary Markov Process ◽  
The Mean

1. This paper was motivated by some questions of Barnett and Lewis (1967) concerning extreme winter temperatures. The temperature during the winter can be hopefully regarded as generated by a stationary Gaussian process superimposed on a locally U-shaped trend. One is interested in statistical properties of the minimum of sample paths from such a process, and of their excursions below a given level. Equivalently one can consider paths from a stationary process crossing a curved boundary of the same form. Problems of this type are discussed by Cramer and Leadbetter (1967), extensively in the trend-free case and in less detail when a trend is present, following the method initiated by Rice (1945). While results on moments are easy to obtain, explicit results for the actual probability distributions are not usually available. However, in the important case when the level of values of interest is far below the mean, the asymptotic independence of up-crossing times makes it possible to derive simple approximate distributions. (See Cramer and Leadbetter (1967) page 256, Keilson (1966).)

The minimum of a stationary Markov process superimposed on a U-shaped trend

1969 ◽  
Vol 6 (2) ◽  
pp. 399-408 ◽  
Author(s):  
H.E. Daniels
Keyword(s):  
Markov Process ◽  
Stationary Process ◽  
Probability Distributions ◽  
Asymptotic Independence ◽  
Curved Boundary ◽  
Sample Paths ◽  
Winter Temperatures ◽  
Free Case ◽  
Stationary Markov Process ◽  
The Mean

1. This paper was motivated by some questions of Barnett and Lewis (1967) concerning extreme winter temperatures. The temperature during the winter can be hopefully regarded as generated by a stationary Gaussian process superimposed on a locally U-shaped trend. One is interested in statistical properties of the minimum of sample paths from such a process, and of their excursions below a given level. Equivalently one can consider paths from a stationary process crossing a curved boundary of the same form. Problems of this type are discussed by Cramer and Leadbetter (1967), extensively in the trend-free case and in less detail when a trend is present, following the method initiated by Rice (1945). While results on moments are easy to obtain, explicit results for the actual probability distributions are not usually available. However, in the important case when the level of values of interest is far below the mean, the asymptotic independence of up-crossing times makes it possible to derive simple approximate distributions. (See Cramer and Leadbetter (1967) page 256, Keilson (1966).)

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

scholarly journals Development of Perceptual Inhibition in Adolescents—a Critical Period?

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 457
Author(s):  
Isabel María Introzzi ◽  
María Marta Richard’s ◽  
Yesica Aydmune ◽  
Eliana Vanesa Zamora ◽  
Florencia Stelzer ◽  
...  
Keyword(s):  
Response Time ◽  
Executive Functions ◽  
Critical Period ◽  
Search Task ◽  
Probability Distributions ◽  
Linear Trajectory ◽  
Gaussian Functions ◽  
Mean Response Time ◽  
The Mean ◽  
One Year

Recent studies suggest that the developmental curves in adolescence, related to the development of executive functions, could be fitted to a non-linear trajectory of development with progressions and retrogressions. Therefore, the present study proposes to analyze the pattern of development in Perceptual Inhibition (PI), considering all stages of adolescence (early, middle, and late) in intervals of one year. To this aim, we worked with a sample of 275 participants between 10 and 25 years, who performed a joint visual and search task (to measure PI). We have fitted ex-Gaussian functions to the probability distributions of the mean response time across the sample and performed a covariance analysis (ANCOVA). The results showed that the 10- to 13-year-old groups performed similarly in the task and differ from the 14- to 19-year-old participants. We found significant differences between the older group and all the rest of the groups. We discuss the important changes that can be observed in relation to the nonlinear trajectory of development that would show the PI during adolescence.

scholarly journals Subcritical Transmission in the Early Stage of COVID-19 in Korea

2021 ◽  
Vol 18 (3) ◽  
pp. 1265
Author(s):  
Yong Sul Won ◽  
Jong-Hoon Kim ◽  
Chi Young Ahn ◽  
Hyojung Lee
Keyword(s):  
Incubation Period ◽  
Early Stage ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Contact Tracing ◽  
Statistical Characterization ◽  
Serial Interval ◽  
Imported Cases ◽  
The Mean ◽  
Reporting Delays

While the coronavirus disease 2019 (COVID-19) outbreak has been ongoing in Korea since January 2020, there were limited transmissions during the early stages of the outbreak. In the present study, we aimed to provide a statistical characterization of COVID-19 transmissions that led to this small outbreak. We collated the individual data of the first 28 confirmed cases reported from 20 January to 10 February 2020. We estimated key epidemiological parameters such as reporting delay (i.e., time from symptom onset to confirmation), incubation period, and serial interval by fitting probability distributions to the data based on the maximum likelihood estimation. We also estimated the basic reproduction number (R0) using the renewal equation, which allows for the transmissibility to differ between imported and locally transmitted cases. There were 16 imported and 12 locally transmitted cases, and secondary transmissions per case were higher for the imported cases than the locally transmitted cases (nine vs. three cases). The mean reporting delays were estimated to be 6.76 days (95% CI: 4.53, 9.28) and 2.57 days (95% CI: 1.57, 4.23) for imported and locally transmitted cases, respectively. The mean incubation period was estimated to be 5.53 days (95% CI: 3.98, 8.09) and was shorter than the mean serial interval of 6.45 days (95% CI: 4.32, 9.65). The R0 was estimated to be 0.40 (95% CI: 0.16, 0.99), accounting for the local and imported cases. The fewer secondary cases and shorter reporting delays for the locally transmitted cases suggest that contact tracing of imported cases was effective at reducing further transmissions, which helped to keep R0 below one and the overall transmissions small.

scholarly journals Perturbation analysis of a variable M/M/1 queue: a probabilistic approach

2006 ◽  
Vol 38 (01) ◽  
pp. 263-283 ◽  
Author(s):  
Nelson Antunes ◽  
Christine Fricker ◽  
Fabrice Guillemin ◽  
Philippe Robert
Keyword(s):  
Power Series ◽  
Busy Period ◽  
Stationary Process ◽  
Probabilistic Approach ◽  
Power Series Expansion ◽  
Mean Value ◽  
Service Rate ◽  
The Mean ◽  
The Impact ◽  
Period Duration

In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.

scholarly journals The prediction model of moisture content’s stabilization during tobacco strip drying process

2018 ◽  
Author(s):  
Mingjian Zhang ◽  
Feng Huang ◽  
Qing Chen ◽  
Le Wang ◽  
Haisheng Wang ◽  
...  
Keyword(s):  
Moisture Content ◽  
Probability Distributions ◽  
Chemical Properties ◽  
Mean Value ◽  
Drying Process ◽  
Variance Model ◽  
Initial Stage ◽  
The Mean ◽  
Agriculture Products ◽  
Physical And Chemical

A mathematical model was established to predict the mean value and variance of tobacco strip during drying processing, based that the physical and chemical properties of tobacco strip as agriculture products show probability distributions. The results show that the model can predict the mean value of moisture content at different times, and there is a certain deviation in predicting the variance of moisture content at initial stage of drying process. However, the prediction value of the variance of tobacco strip is much more accurate while the moisture content is between 8% and 10%, which is the interval of quality requirements.Keywords: tobacco strip; drying; mean value;variance model.  

scholarly journals Lattice Paths, Sampling Without Replacement, and Limiting Distributions

10.37236/156 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
M. Kuba ◽  
A. Panholzer ◽  
H. Prodinger
Keyword(s):  
Generating Functions ◽  
Probability Distributions ◽  
Random Variable ◽  
Phase Changes ◽  
Lattice Paths ◽  
Sampling Without Replacement ◽  
Sample Paths ◽  
Quarter Plane ◽  
Explicit Formulae ◽  
Weighted Lattice Paths

In this work we consider weighted lattice paths in the quarter plane ${\Bbb N}_0\times{\Bbb N}_0$. The steps are given by $(m,n)\to(m-1,n)$, $(m,n)\to(m,n-1)$ and are weighted as follows: $(m,n)\to(m-1,n)$ by $m/(m+n)$ and step $(m,n)\to(m,n-1)$ by $n/(m+n)$. The considered lattice paths are absorbed at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$. We provide explicit formulæ for the sum of the weights of paths, starting at $(m,n)$, which are absorbed at a certain height $k$ at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$, using a generating functions approach. Furthermore these weighted lattice paths can be interpreted as probability distributions arising in the context of Pólya-Eggenberger urn models, more precisely, the lattice paths are sample paths of the well known sampling without replacement urn. We provide limiting distribution results for the underlying random variable, obtaining a total of five phase changes.

THE EFFECTS OF TEMPERATURE ON THE OXYGEN CONSUMPTION, HEART RATE AND DEEP BODY TEMPERATURE DURING DIVING IN THE TUFTED DUCK AYTHYA FULIGULA

1992 ◽  
Vol 163 (1) ◽  
pp. 139-151 ◽  
Author(s):  
R. M. BEVAN ◽  
P. J. BUTLER
Keyword(s):  
Oxygen Consumption ◽  
Body Temperature ◽  
Deep Body Temperature ◽  
Tufted Duck ◽  
Winter Conditions ◽  
Winter Temperatures ◽  
Summer Temperatures ◽  
The Mean ◽  
Maintain Body Temperature ◽  
Deep Body

Six tufted ducks were trained to dive for food at summer temperatures (air, 26°C, water, 23°C) and at winter temperatures (air, 5.8°C, water 7.4°C). The mean resting oxygen consumption (Voo2) a t winter temperatures (rwin) was 90% higher than that at summer temperatures (Tsum), but deep body temperatures (Tb) were not significantly different. Diving behaviour and mean oxygen consumption for dives of mean duration were similar at Twin and at Tsum, although the mean oxygen consumption for surface intervals of mean duration was 50% greater at Twin and Tb was significantly lower (1°C) at the end of a series of dives in winter than it was in summer. There appears to be an energy saving of 67 J per dive during winter conditions and this may, at least partially, be the result of the metabolic heat produced by the active muscles being used to maintain body temperature. While at rest under winter conditions, this would be achieved by shivering thermogenesis. Thus, the energetic costs of foraging in tufted ducks in winter are not as great as might be expected from the almost doubling of metabolic rate in resting birds.

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