Measuring the probability distribution of the absolute maxima of excursions of random processes

1983 ◽  
Vol 26 (5) ◽  
pp. 341-343
Author(s):  
V. I. Potapkin ◽  
V. A. Rakov
Keyword(s):  
Probability Distribution ◽  
Random Processes ◽  
The Absolute

Extreme Values of Waves and Ship Responses Subject to the Markov Chain Condition

1979 ◽  
Vol 23 (03) ◽  
pp. 188-197
Author(s):  
Michel K. Ochi
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Probability Distribution ◽  
Random Process ◽  
Probability Distribution Function ◽  
Extreme Values ◽  
Random Processes ◽  
Chain Condition ◽  
Extreme Value ◽  
Spectral Bandwidth

This paper discusses the effect of statistical dependence of the maxima (peak values) of a stationary random process on the magnitude of the extreme values. A theoretical analysis of the extreme values of a stationary normal random process is made, assuming the maxima are subject to the Markov chain condition. For this, the probability distribution function of maxima as well as the joint probability distribution function of two successive maxima of a normal process having an arbitrary spectral bandwidth are applied to Epstein's theorem for evaluating the extreme values in a given sample under the Markov chain condition. A numerical evaluation of the extreme values is then carried out for a total of 14 random processes, including nine ocean wave records, with various spectral bandwidth parameters ranging from 0.11 to 0.78. From the results of the computations, it is concluded that the Markov concept is applicable to the maxima of random processes whose spectral bandwidth parameter, ɛ, is less than 0.5, and that the extreme values with and without the Markov concept are constant irrespective of the e-value, and the former is approximately 10 percent greater than the latter. It is also found that the sample size for which the extreme value reaches a certain level with the Markov concept is much less than that without the Markov concept. For example, the extreme value will reach a level of 4.0 (nondimensional value) in 1100 observations of the maxima with the Markov concept, while the extreme value will reach the same level in 3200 observations of the maxima without the Markov concept.

scholarly journals EFFECTS OF INTRADAY PATTERNS ON ANALYSIS OF STOCK MARKET INDEX AND TRADING VOLUME

2012 ◽  
Vol 16 ◽  
pp. 41-50
Author(s):  
HYUNG WOOC CHOI ◽  
SEONG EUN MAENG ◽  
JAE WOO LEE
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Probability Distribution ◽  
Stock Market ◽  
Power Law ◽  
Volume Change ◽  
Probability Distribution Function ◽  
Stock Index ◽  
The Absolute ◽  
Intraday Patterns

We review the stylized properties of the stock market and consider effects of the intraday patterns on the analysis of the time series for the stock index and the trading volume in Korean stock market. In the stock market the probability distribution function (pdf) of the return and volatility followed the power law for the stock index and the change of the volume traded. The volatility of the stock index showed the long-time memory and the autocorrelation function followed a power law. We applied two eliminating methods of the intraday patterns: the intraday patterns of the time series itself, and the intraday patterns of the absolute return for the index or the absolute volume change. We scaled the index and return by two types of the intraday patterns. We considered the probability distribution function and the autocorrelation function (ACF) for the time series scaled by the intraday patterns. The cumulative probability distribution function of the returns scaled by the intraday patterns showed a power law, P>(r) ~ r-α±, where α± corresponds to the exponent of the positive and negative fat tails. The pdf of the return scaled by intraday patterns by the absolute return decayed much steeper than that of the return scaled by intraday patterns of the index itself. The pdf for the volume change also followed the power law for both methods of eliminating intraday patterns. However, the exponents of the power law at fat tails do not depend on the intraday patterns. The ACF of the absolute return showed long-time correlation and followed the power law for the scaled index and for the scaled volume. The daily periodicity of the ACF was removed for scaled time series by the intraday patterns of the absolute return or the absolute volume change.

A mathematical model of an oil and gas field development process

2010 ◽  
Vol 21 (3) ◽  
pp. 205-227 ◽  
Author(s):  
C. ATKINSON ◽  
R. ISANGULOV
Keyword(s):  
Mathematical Model ◽  
Probability Distribution ◽  
Development Process ◽  
Oil And Gas ◽  
Renewal Theory ◽  
Random Processes ◽  
Gas Field ◽  
Field Development ◽  
Oil And Gas Field ◽  
Complete Probability

A mathematical model of the development of an oil and gas field is presented. The field development process is treated as sequential in nature. Completion of a well and its production are considered to be random processes. The model uses results from renewal theory where the completion of a well and failure to produce economical amount of oil or gas are analogous to the failure of a component. In principle, the theory described can give the complete probability distribution associated with a field development. Explicit expressions are given for the expected value and variance of the number of completed wells.

Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sayan Gupta ◽  
P. H. A. J. M. van Gelder
Keyword(s):  
Probability Distribution ◽  
Gaussian Process ◽  
Joint Probability ◽  
Random Processes ◽  
Von Mises Stress ◽  
Analytical Approximations ◽  
Multidimensional Integration ◽  
Reliability Method ◽  
Non Gaussian ◽  
Von Mises

The problem of approximating the probability distribution of peaks, associated with a special class of non-Gaussian random processes, is considered. The non-Gaussian processes are obtained as nonlinear combinations of a vector of mutually correlated, stationary, Gaussian random processes. The Von Mises stress in a linear vibrating structure under stationary Gaussian loadings is a typical example for such processes. The crux of the formulation lies in developing analytical approximations for the joint probability density function of the non-Gaussian process and its instantaneous first and second time derivatives. Depending on the nature of the problem, this requires the evaluation of a multidimensional integration across a possibly irregular and disjointed domain. A numerical algorithm, based on first order reliability method, is developed to evaluate these integrals. The approximations for the peak distributions have applications in predicting the expected fatigue damage due to combination of stress resultants in a randomly vibrating structure. The proposed method is illustrated through two numerical examples and its accuracy is examined with respect to estimates from full scale Monte Carlo simulations of the non-Gaussian process.

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