On Computing Critical Points for a Bivariate Chi-Square Random Variable

1973 ◽  
Vol 2 (3) ◽  
pp. 221-224
Author(s):  
Richard Gunst
Keyword(s):  
Critical Points ◽  
Random Variable ◽  
Chi Square

TESTING CHAOS OF TIME SERIES: PORTMANTEAU STATISTICS UNDER AN ORDER TRANSFORMATION

2001 ◽  
Vol 11 (06) ◽  
pp. 1761-1769 ◽  
Author(s):  
DEJIAN LAI
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Random Variable ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Chi Square ◽  
Gaussian Series ◽  
Low Dimensional ◽  
Portmanteau Statistics ◽  
Direct Use

This paper studies several portmanteau test statistics with a nonparametric order transformation for distinguishing independent and identically distributed (i.i.d.) random processes from noisy chaotic time series. These portmanteau test statistics are asymptotically distributed as a chi-square random variable under the null hypothesis of i.i.d. Gaussian series. In this Letter, we show that the asymptotic distributions of these portmanteau test statistics on the transformed series are still chi-square under the null hypothesis. The simulations indicate that direct use of these portmanteau test statistics yields low power in identifying chaos. However, with the proposed order transformation, the simulations show that these test statistics are still effective for identifying noisy low dimensional chaos in some cases.

A Chi-Square Distribution Based Steady-State Data Judgment Criterion

2011 ◽  
Vol 80-81 ◽  
pp. 724-729
Author(s):  
Jie Su ◽  
Xu Guang Wang
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Working Condition ◽  
Random Variable ◽  
Chi Square ◽  
State Data ◽  
Large Probability ◽  
Variation Range ◽  
Self Adaptive

The acquisition of steady-state data is the premise for optimizing the boiler combustion parameters. Assuming the measuring parameters obey the Gaussion distribution, this paper uses the large-probability distribution interval to approximate the variation range of random variable, constructs appropriate working condition matrix whose column quadratic sum approximately obeys the Chi-square distribution, and then obtains the Chi-square distribution based steady-state data judgment criterion. The judgment threshold of this criterion could be self-adaptive. This judgment criterion has been validated by an experiment.

WICK CALCULUS FOR THE SQUARE OF A GAUSSIAN RANDOM VARIABLE WITH APPLICATION TO YOUNG AND HYPERCONTRACTIVE INEQUALITIES

2012 ◽  
Vol 15 (03) ◽  
pp. 1250018 ◽  
Author(s):  
ALBERTO LANCONELLI ◽  
LUIGI SPORTELLI
Keyword(s):  
Gaussian Measure ◽  
Type Inequality ◽  
Random Variable ◽  
Gaussian Random Variable ◽  
Wick Product ◽  
Probabilistic Interpretation ◽  
Chi Square ◽  
Wick Calculus

We investigate a probabilistic interpretation of the Wick product associated to the chi-square distribution in the spirit of the results obtained in Ref. 7 for the Gaussian measure. Our main theorem points out a profound difference from the previously studied Gaussian7 and Poissonian12 cases. As an application, we obtain a Young-type inequality for the Wick product associated to the chi-square distribution which contains as a particular case a known Nelson-type hypercontractivity theorem.

scholarly journals Minimum noiseless description length (MNDL) thresholding

2021 ◽  
Author(s):  
Azadeh Fakhrzadeh
Keyword(s):  
Image Denoising ◽  
Additive Noise ◽  
Random Variable ◽  
Data Driven ◽  
Mean Square ◽  
Chi Square ◽  
Denoising Method ◽  
Thresholding Method ◽  
Simulation Results ◽  
Subspace Selection

In this thesis, the problem of data denoising is considered and a new data denoising method is developed. This approach is an adaptive, data-driven thresholding method that is based on Minimum Noiseless Description Length (MNDL). MNDL is an approach to subspace selection which estimates bounds on the desired Mean Square Error (MSE). The subspace minimizing these bounds is chosen as the optimum one. In this research, we explore application of MNDL Subspace Selection (MNDL-SS) as a thresholding method. Although the basic idea and desired criterion of MNDL thresholding and MNDL-SS are the same, the challenges in calculation of the desired criterion in MNDL thresholding are very different. In MNDL-SS, the additive noise effects are in the form of samples of a Chi-Square random variable. However, this assumption does not hold for MNDL thresholding anymore. In this research, we developed a new method for calculation of the desired criterion based on characteristics of noise in thresholding. Our simulation results show that MNDL thresholding outperforms the compared methods. In this thesis, we also explore the area of image denoising. In image denoising approaches, some properties of the image are considered. One of the well known image denoising methods, that outperforms other methods, is BayesShrink. We compare our method with BayesShrink. We show that the results of MNDS thresholding are comparable with BayesShrink in our simulations.

A Note On The Calculation And Application Of The Third Absolute Central Moment Of Chi-square Distribution

1992 ◽  
pp. 83-86
Author(s):  
Abu Hassan Shaari Mohd Nor ◽  
Fauziah Maarof
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variable ◽  
Central Moment ◽  
Chi Square ◽  
Exact Bound ◽  
The Third ◽  
The Central Limit Theorem ◽  
Numerical Integrations

Kertas ini mengemukakan satu cara mencari momen memusat mutlak ketiga bagi pembolehubah rawak khi-kuasadua. Aturcara SAS (1988) iaitu PROBCHI digunakan bagi menyelesaikan pengamiran berangka. Kegunaannya dalam membina batas yang tepat ke atas ralat penghampiran dalam Teorem Had Memusat diberikan. This paper presents a way of calculating the third absolute central moment of a chi-square random variable. The SAS (1988) function PROBCHI is used to evaluate the numerical integrations. An application of this result in the construction of an exact bound on the error of approximation in the Central Limit Theorem is presented.

scholarly journals Minimum noiseless description length (MNDL) thresholding

2021 ◽  
Author(s):  
Azadeh Fakhrzadeh
Keyword(s):  
Image Denoising ◽  
Additive Noise ◽  
Random Variable ◽  
Data Driven ◽  
Mean Square ◽  
Chi Square ◽  
Denoising Method ◽  
Thresholding Method ◽  
Simulation Results ◽  
Subspace Selection

In this thesis, the problem of data denoising is considered and a new data denoising method is developed. This approach is an adaptive, data-driven thresholding method that is based on Minimum Noiseless Description Length (MNDL). MNDL is an approach to subspace selection which estimates bounds on the desired Mean Square Error (MSE). The subspace minimizing these bounds is chosen as the optimum one. In this research, we explore application of MNDL Subspace Selection (MNDL-SS) as a thresholding method. Although the basic idea and desired criterion of MNDL thresholding and MNDL-SS are the same, the challenges in calculation of the desired criterion in MNDL thresholding are very different. In MNDL-SS, the additive noise effects are in the form of samples of a Chi-Square random variable. However, this assumption does not hold for MNDL thresholding anymore. In this research, we developed a new method for calculation of the desired criterion based on characteristics of noise in thresholding. Our simulation results show that MNDL thresholding outperforms the compared methods. In this thesis, we also explore the area of image denoising. In image denoising approaches, some properties of the image are considered. One of the well known image denoising methods, that outperforms other methods, is BayesShrink. We compare our method with BayesShrink. We show that the results of MNDS thresholding are comparable with BayesShrink in our simulations.

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