A Comparison of Alternative Approaches for the Synthetic Generation of a Wind Speed Time Series

1991 ◽  
Vol 113 (4) ◽  
pp. 280-289 ◽  
Author(s):  
F. C. Kaminsky ◽  
R. H. Kirchhoff ◽  
C. Y. Syu ◽  
J. F. Manwell
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Wind Speed ◽  
Probability Distribution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Statistical Properties ◽  
Embedded Markov Chain ◽  
One Step ◽  
Alternative Approaches

In this paper, alternative approaches for synthetically generating a wind speed time series are discussed. These approaches include: (1) the use of independent values from a specific probability distribution; (2) the use of an algorithm based on the statistical behavior of a one-step Markov chain; (3) the use of an algorithm based on the behavior of a transition probability matrix that describes the next wind speed value statistically as a function of the current wind speed value and the previous wind speed value; (4) the use of Box-Jenkins models; (5) the use of the Shinozuka algorithm; and (6) the use of an embedded Markov chain. The ability of each approach to capture the statistical properties of the desired wind speed time series is discussed. In this context the statistical properties of interest are the probability distribution of the wind speed values, the autocorrelation function of the wind speed values, and the spectral density of the wind speed values.

The censored Markov chain and the best augmentation

1996 ◽  
Vol 33 (03) ◽  
pp. 623-629 ◽  
Author(s):  
Y. Quennel Zhao ◽  
Danielle Liu
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
The Best Approximation ◽  
Finite Matrix ◽  
Countable State ◽  
Stationary Probabilities

Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

scholarly journals On the Convergence Rate of Bonus-Malus Systems

1992 ◽  
Vol 22 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Heikki Bonsdorff
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Convergence Rate ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Limit Probability ◽  
Step Transition

AbstractUnder certain conditions, a Bonus-Malus system can be interpreted as a Markov chain whose n-step transition probabilities converge to a limit probability distribution. In this paper, the rate of the convergence is studied by means of the eigenvalues of the transition probability matrix of the Markov chain.

Finite dams with inputs forming a Markov chain

1970 ◽  
Vol 7 (02) ◽  
pp. 291-303 ◽  
Author(s):  
M.S. Ali Khan
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Generating Functions ◽  
State Transition ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Time Dependent ◽  
Probability Generating Functions ◽  
State Transition Probability ◽  
Finite Dam

This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.

Finite dams with inputs forming a Markov chain

1970 ◽  
Vol 7 (2) ◽  
pp. 291-303 ◽  
Author(s):  
M.S. Ali Khan
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Generating Functions ◽  
State Transition ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Time Dependent ◽  
Probability Generating Functions ◽  
State Transition Probability ◽  
Finite Dam

This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.

A note on cumulative sums of markovian variables

1965 ◽  
Vol 5 (2) ◽  
pp. 285-287 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Finite Number ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
The Matrix ◽  
Initial Probability Distribution ◽  
Regular Markov Chain ◽  
Image Position ◽  
Cumulative Sums

Consider a positive regular Markov chain X0, X1, X2,… with s(s finite) number of states E1, E2,… E8, and a transition probability matrix P = (pij) where = , and an initial probability distribution given by the vector p0. Let {Zr} be a sequence of random variables such that and consider the sum SN = Z1+Z2+ … ZN. It can easily be shown that (cf. Bartlett [1] p. 37), where λ1(t), λ2(t)…λ1(t) are the latent roots of P(t) ≡ (pijethij) and si(t) and t′i(t) are the column and row vectors corresponding to λi(t), and so constructed as to give t′i(t)Si(t) = 1 and t′i(t), si(o) = si where t′i(t) and si are the corresponding column and row vectors, considering the matrix .

scholarly journals Correlated random walks with stay

1988 ◽  
Vol 1 (3) ◽  
pp. 197-222
Author(s):  
Ram Lal ◽  
U. Narayan Bhat
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Equilibrium Solution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Finite State ◽  
Direction Of Movement ◽  
One Step ◽  
Bivariate Markov Chain

A random walk describes the movement of a particle in discrete time, with the direction and the distance traversed in one step being governed by a probability distribution. In a correlated random walk (CRW) the movement follows a Markov chain and induces correlation in the state of the walk at various epochs. Then, the walk can be modelled as a bivariate Markov chain with the location of the particle and the direction of movement as the two variables. In such random walks, normally, the particle is not allowed to stay at one location from one step to the next. In this paper we derive explicit results for the following characteristics of the CRW when it is allowed to stay at the same location, directly from its transition probability matrix: (i) equilibrium solution and the fast passage probabilities for the CRW restricted on one side, and (ii) equilibrium solution and first passage characteristics for the CRW restricted on bath sides (i.e., with finite state space).

Prediction of Displacement Time Series Based on Support Vector Machines-Markov Chain

2014 ◽  
Vol 580-583 ◽  
pp. 436-439 ◽  
Author(s):  
Fei Xu ◽  
Wen Xiong Xu ◽  
Ke Wang
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Support Vector Machines ◽  
Transition Probability ◽  
Absolute Error ◽  
Transition Probability Matrix ◽  
Support Vector ◽  
State Transition Probability ◽  
Vector Machines ◽  
Measured Displacement

A new displacement time series predicting model was proposed by combining the Support Vector Machines and the Markov Chain, which was named as Support Vector Machines and Markov Chain (SVM-MC) model. Through studying the measured displacement, SVM optimized by particle swarm optimization (PSO) was used to forecast the trend of macro development in roll. Markov chain was applied to compute State Transition Probability Matrix. By classifying system state and calculating absolute error and relative error between measured value and SVM fitting value, the predicting results are improved. The model was used on predicting displacement time series of a high slope of a permanent lock. The engineering case studies indicated that the model was scientific and reliable, and there was engineering practical value for displacement time series forecasting.

The censored Markov chain and the best augmentation

1996 ◽  
Vol 33 (3) ◽  
pp. 623-629 ◽  
Author(s):  
Y. Quennel Zhao ◽  
Danielle Liu
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
The Best Approximation ◽  
Finite Matrix ◽  
Countable State ◽  
Stationary Probabilities

Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

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