scholarly journals Research on drought in southwest China based on the theory of run and two-dimensional joint distribution theory

2014 ◽  
Vol 63 (23) ◽  
pp. 230204
Author(s):  
Zuo Dong-Dong ◽  
Hou Wei ◽  
Yan Peng-Cheng ◽  
Feng Tai-Chen
Keyword(s):  
Joint Distribution ◽  
Southwest China ◽  
Distribution Theory ◽  
Two Dimensional

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

The Two-Dimensional Histogram as a Constraint for Protein Phase Improvement

1998 ◽  
Vol 54 (6) ◽  
pp. 1230-1244 ◽  
Author(s):  
Alexandra Goldstein ◽  
Kam Y. J. Zhang
Keyword(s):  
Standard Deviation ◽  
Correlation Coefficient ◽  
Electron Density ◽  
Joint Distribution ◽  
Phase Error ◽  
Temperature Factor ◽  
Two Dimensional ◽  
Average Correlation ◽  
Phase Selection ◽  
2D Histogram

The joint distribution of electron density and its gradient in a protein electron-density map was examined. This joint distribution was represented by a two-dimensional histogram (2D histogram) of electron-density values and the modulus of the gradient. 16 structures representing distinct protein-fold families were selected to study the dependence of the 2D histogram on resolution, overall temperature factor, structural conformation and phase error. The similarity between the histograms for a pair of structures was measured by correlation coefficient, and the residual provided a measure of the difference. The 2D histogram was found to vary with resolution and overall temperature factor, but was found to be insensitive to structure conformation. The average correlation coefficient between pairs of 2D histograms at three different resolutions examined was 0.90 with a standard deviation of 0.04. The average residual for the same condition was 0.13 with a standard deviation of 0.03. The 2D histogram was also found to be sensitive to phase error. The average correlation coefficient and residual between 2D histograms with 10° phase difference are 0.71 and 0.18, respectively. The variation of the 2D histogram resulting from structure-conformation changes was estimated to be equivalent to that of a 4° phase error. This establishes the minimal phase error that a 2D histogram-matching method could achieve. The conservation of the 2D histogram with respect to structure conformation enables the prediction of the ideal 2D histogram for unknown structures. The sensitivity of the 2D histogram to phase error suggests that it could be used as a target for the density-modification method and also could be used as a figure of merit for phase selection in ab initio phasing.

Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process

2003 ◽  
Vol 35 (3) ◽  
pp. 551-562 ◽  
Author(s):  
Pierre Calka
Keyword(s):  
Fundamental Domain ◽  
Joint Distribution ◽  
Voronoi Tessellation ◽  
Two Dimensional ◽  
Integral Expression ◽  
Geometric Characteristics ◽  
Typical Cell ◽  
Line Process ◽  
Poisson Line Process

In this paper, we give an explicit integral expression for the joint distribution of the number and the respective positions of the sides of the typical cell 𝒞 of a two-dimensional Poisson-Voronoi tessellation. We deduce from it precise formulae for the distributions of the principal geometric characteristics of 𝒞 (area, perimeter, area of the fundamental domain). We also adapt the method to the Crofton cell and the empirical (or typical) cell of a Poisson line process.

The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane

2002 ◽  
Vol 34 (04) ◽  
pp. 702-717 ◽  
Author(s):  
Pierre Calka
Keyword(s):  
Joint Distribution ◽  
Voronoi Tessellation ◽  
Two Dimensional ◽  
Conditional Probabilities ◽  
Polygonal Cell ◽  
Typical Particle ◽  
Covering Properties ◽  
Typical Cell ◽  
Line Process ◽  
Poisson Line Process

Among the disks centered at a typical particle of the two-dimensional Poisson-Voronoi tessellation, letRmbe the radius of the largest included within the polygonal cell associated with that particle andRMbe the radius of the smallest containing that polygonal cell. In this article, we obtain the joint distribution ofRmandRM. This result is derived from the covering properties of the circle due to Stevens, Siegel and Holst. The same method works for studying the Crofton cell associated with the Poisson line process in the plane. The computation of the conditional probabilities P{RM≥r+s|Rm=r} reveals the circular property of the Poisson-Voronoi typical cells (as well as the Crofton cells) having a ‘large’ in-disk.

scholarly journals Renewal theory in two dimensions: asymptotic results

1974 ◽  
Vol 6 (3) ◽  
pp. 546-562 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Joint Distribution ◽  
Counting Process ◽  
Renewal Theory ◽  
Two Dimensions ◽  
Renewal Processes ◽  
Unified Theory ◽  
Two Dimensional ◽  
Renewal Function ◽  
Asymptotic Results ◽  
Renewal Counting Process

In an earlier paper (Renewal theory in two dimensions: Basic results) the author developed a unified theory for the study of bivariate renewal processes. In contrast to this aforementioned work where explicit expressions were obtained, we develop some asymptotic results concerning the joint distribution of the bivariate renewal counting process (Nx(1), Ny(2)), the distribution of the two-dimensional renewal counting process Nx,y and the two-dimensional renewal function &Nx,y. A by-product of the investigation is the study of the distribution and moments of the minimum of two correlated normal random variables. A comprehensive bibliography on multi-dimensional renewal theory is also appended.

The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane

2002 ◽  
Vol 34 (4) ◽  
pp. 702-717 ◽  
Author(s):  
Pierre Calka
Keyword(s):  
Joint Distribution ◽  
Voronoi Tessellation ◽  
Two Dimensional ◽  
Conditional Probabilities ◽  
Polygonal Cell ◽  
Typical Particle ◽  
Covering Properties ◽  
Typical Cell ◽  
Line Process ◽  
Poisson Line Process

Among the disks centered at a typical particle of the two-dimensional Poisson-Voronoi tessellation, let Rm be the radius of the largest included within the polygonal cell associated with that particle and RM be the radius of the smallest containing that polygonal cell. In this article, we obtain the joint distribution of Rm and RM. This result is derived from the covering properties of the circle due to Stevens, Siegel and Holst. The same method works for studying the Crofton cell associated with the Poisson line process in the plane. The computation of the conditional probabilities P{RM ≥ r + s | Rm = r} reveals the circular property of the Poisson-Voronoi typical cells (as well as the Crofton cells) having a ‘large’ in-disk.

scholarly journals Calculation of Joint Return Period for Connected Edge Data

Water ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 300 ◽  
Author(s):  
Guilin Liu ◽  
Baiyu Chen ◽  
Zhikang Gao ◽  
Hanliang Fu ◽  
Song Jiang ◽  
...  
Keyword(s):  
Wind Speed ◽  
Correlation Analysis ◽  
Wave Height ◽  
Joint Distribution ◽  
Measured Data ◽  
Two Dimensional ◽  
Ocean Engineering ◽  
Extreme Wave ◽  
Correlation Measure ◽  
Copula Functions

For better displaying the statistical properties of measured data, it is particularly important to select a suitable multivariate joint distribution model in ocean engineering. According to the characteristics and properties of Copula functions and the correlation analysis of measured data, the nonlinear relationship between random variables can be captured. Additionally, the models based on the Copula theory have more general applicability. A series of correlation measure index, derived from Copula functions, can expand the correlation measure range among variables. In this paper, by means of the correlation analysis between the annual extreme wave height and the corresponding wind speed, their joint distribution models were studied. The newly established two-dimensional joint distribution functions of the extreme wave height and the corresponding wind speed were compared with the existing two-dimensional joint distributions.

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