Markovian chi-square and gamma processes

Adke, S. R.; Balakrishna, N.

doi:10.1016/0167-7152(92)90152-u

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…Lawrance and Lewis, in a series of papers, have discussed several autoregressive moving average (ARMA(1,1)) sequences with exponential and gamma marginals; see the work of Lawrance and Lewis and the references contained therein. Properties of other Markov sequences with non‐Gaussian marginals such as gamma (see the work of Sim and Adke and Balakrishna), inverse Gaussian (see the work of Abraham and Balakrishna), Cauchy (see the work of Balakrishna and Nampoothiri), normal‐Laplace (see the work of Jose et al), beta distribution (see the work of Rocha and Cribari‐Neto), approximate beta distribution (see the works of Popovic et al()), and extreme value (see the work of Balakrishna and Shiji) have also been discussed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Time series with Birnbaum‐Saunders marginal distributions

Rahul

Balakrishna

2018

Appl Stoch Models Bus & Ind

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A stationary sequence of random variables with Birnbaum-Saunders marginal distribution is constructed using a Gaussian autoregressive moving average sequence. The parameters of the model are then estimated by the maximum likelihood method, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is carried out to assess the performance of the estimators. The proposed model is finally used to analyze 2 real data sets. KEYWORDS autoregressive moving average models, Birnbaum-Saunders distribution, consistent and asymptotically normal, maximum likelihood estimators, non-Gaussian time series 562

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Section: Introductionmentioning

confidence: 99%

Time series with Birnbaum‐Saunders marginal distributions

Rahul

Balakrishna

2018

Appl Stoch Models Bus & Ind

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“…The usual techniques of transforming the data to use a Gaussian model also fail in certain situations (see Lawrance, 1991). Hence, a number of non-Gaussian time series models have been introducted by different researchers during the last two decades (see for example Lawrance and Lewis, 1985;Adke and Balakrishna, 1992a; and references there).…”

Section: Introductionmentioning

confidence: 99%

Inverse Gaussian Autoregressive Models

Abraham

Balakrishna

1999

Journal Time Series Analysis

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“…Some work has appeared on gamma processes [10], but LCRs do not appear to be available. However, for the special case of a chi-squared (χ 2 ) process, the LCR is known [11].…”

Section: Level Crossing Ratesmentioning

confidence: 99%

Level crossing rates for MIMO channel Eigenvalues: implications for adaptive systems

Smith

Kuo

Garth

IEEE International Conference on Communications, 2005. ICC 2005. 2005

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Abstract-MIMO systems using adaptive transmission down the eigenchannels require the level crossing rate of the eigenvalues to compute adaptation rates and possibly feedback rates. Examples of such systems include MIMO systems using singular value decomposition (SVD) transmission. Similarly, the average fade durations of the eigenvalues give the average length of time that a particular constellation is used in adaptive modulation. Other systems which require the minimum eigenvalue to be above a certain threshold (for example, channel inversion) can also use these level crossing rates in system analysis. Hence, in this paper we derive approximate level crossing rates for the eigenvalues in the baseline case of an uncorrelated Rayleigh fading channel. Our results are remarkably accurate and compact and further improvements are also discussed.

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Markovian chi-square and gamma processes

Cited by 7 publications

References 7 publications

Time series with Birnbaum‐Saunders marginal distributions

Time series with Birnbaum‐Saunders marginal distributions

Inverse Gaussian Autoregressive Models

Level crossing rates for MIMO channel Eigenvalues: implications for adaptive systems

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