Statistical Analysis for the Duration and Time Intervals of Tropical Cyclones, Hong Kong

2019 ◽  
Author(s):  
Shanshan Tao ◽  
Jialing Song ◽  
Zhifeng Wang ◽  
Yong Liu ◽  
Sheng Dong
Keyword(s):  
Hong Kong ◽  
Tropical Cyclone ◽  
Probability Distribution ◽  
Tropical Cyclones ◽  
Conditional Probability ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Time Intervals

Abstract Hong Kong is impacted by tropical cyclones from April to December each year. The duration of tropical cyclones is one key factor to impact the normal operation of port or coastal engineering, and longer time interval between two tropical cyclones can provide longer operation or construction time. Therefore, it is quite important to study on the long-term laws of the duration and time intervals of tropical cyclones which attacked Hong Kong. The Hong Kong Observatory issues the warning signals to warn the public of the threat of winds associated with a tropical cyclone. Choose the tropical cyclones with warning signal No. 3 or above as the research object. A statistical study was conducted on the duration of each tropical cyclone, the time interval between every two continuous tropical cyclones during the year, and the time interval between the last cyclone of each year and the first cyclone of the following year. Poisson compound extreme value distributions are constructed to calculate the return values, which can make people know how long a tropical cyclone with a fixed duration or time interval occurs once in statistical average sense. Based on bivariate copulas, the joint probability distribution of duration and time intervals of tropical cyclones are presented. Then when the duration of a tropical cyclone is known, the conditional probability that the time interval before the next tropical cyclone occurs is greater than a certain value can be calculated. The results provide corresponding conditional probability distributions. Similarly, for the sum of the duration of tropical cyclones each year, and the time interval between the last cyclone of each year and the first cyclone of the following year, their joint probability distribution and conditional probability distributions are also presented. The conditional probability can provide the probabilistic prediction of the length of the stationary period (with no impact of tropical cyclones).

scholarly journals Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging

2019 ◽  
Vol 23 ◽  
pp. 271-309
Author(s):  
Joseph Muré
Keyword(s):  
Probability Distribution ◽  
Gibbs Sampler ◽  
Prediction Interval ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Distributions ◽  
Stationary Probability Distribution ◽  
Gibbs Sampling Algorithm ◽  
Correlation Parameters

Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.

Study on the joint probability distribution of irrigation water volume and irrigation water efficiency

2015 ◽  
Vol 15 (4) ◽  
pp. 802-809
Author(s):  
Yong Zhao ◽  
Jinping Zhang ◽  
Weihua Xiao
Keyword(s):  
Probability Distribution ◽  
Conditional Probability ◽  
Irrigation Water ◽  
Joint Probability ◽  
Water Volume ◽  
Joint Probability Distribution ◽  
Water Efficiency ◽  
Copula Method ◽  
Joint Return ◽  
Water Volumes

Using the copula method, the joint probability distribution of irrigation water volume and efficiency is constructed, and their joint return period is also described to reveal the encounter probability of irrigation water volume and efficiency. Furthermore, the conditional probability of irrigation water efficiency with different water volumes is built to show the quantitative effects of flow on irrigation water efficiency. The results show that the copula-based function can present the encounter risk and conditional probability of irrigation water volume and efficiency at their different magnitudes.

scholarly journals Tests for quantum contextuality in terms of Q-entropies

2014 ◽  
Vol 14 (11&12) ◽  
pp. 996-1013
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Theoretic Approach ◽  
Entropic Inequalities ◽  
Information Theoretic ◽  
The Family ◽  
Information Theoretic Approach ◽  
New Inequalities

The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser--Horne--Shimony--Holt (CHSH) and Klyachko--Can--Binicio\v{g}lu--Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.

Pseudo Independent Models

2011 ◽  
pp. 935-940
Author(s):  
Yang Xiang
Keyword(s):  
Probability Distribution ◽  
Computer System ◽  
Conditional Probability ◽  
Graphical Models ◽  
Intelligent Systems ◽  
Probabilistic Reasoning ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Probability Distribution ◽  
Binary Variables

Graphical models such as Bayesian networks (BNs) (Pearl, 1988) and decomposable Markov networks (DMNs) (Xiang, Wong & Cercone, 1997) have been applied widely to probabilistic reasoning in intelligent systems. Figure1 illustrates a BN and a DMN on a trivial uncertain domain: A virus can damage computer files, and so can a power glitch. A power glitch also causes a VCR to reset. The BN in (a) has four nodes, corresponding to four binary variables taking values from {true, false}. The graph structure encodes a set of dependence and independence assumptions (e.g., that f is directly dependent on v, and p but is independent of r, once the value of p is known). Each node is associated with a conditional probability distribution conditioned on its parent nodes (e.g., P(f | v, p)). The joint probability distribution is the product P(v, p, f, r) = P(f | v, p) P(r | p) P(v) P(p). The DMN in (b) has two groups of nodes that are maximally pair-wise connected, called cliques. Each clique is associated with a probability distribution (e.g., clique {v, p, f} is assigned P(v, p, f)). The joint probability distribution is P(v, p, f, r) = P(v, p, f) P(r, p) / P(p), where P(p) can be derived from one of the clique distributions. The networks, for instance, can be used to reason about whether there are viruses in the computer system, after observations on f and r are made.

Joint probability of storm surge and wave along Hainan Island based on bi-variate copulas analysis

2020 ◽  
Author(s):  
Meng Cheng ◽  
Weihua Fang
Keyword(s):  
Probability Distribution ◽  
Storm Surge ◽  
Wave Height ◽  
Significant Wave Height ◽  
Probability Distributions ◽  
Joint Probability ◽  
Hainan Island ◽  
Joint Probability Distribution ◽  
Significant Wave ◽  
Surge Height

<p>Tropical cyclones (TCs) often bring multiple hazards to offshore and onshore areas, including wind, rainfall, riverine flood, wave and storm surge. These hazards usually interact with each other and cause greater amplified hazard intensity. In the coastal areas, wave may damage coastal defense system like sea walls and dykes, and overtopping storm surge could hence become severe flooding due to the breach of the dykes. The probability distributions of wave and surge, as univariate respectively, have been studies and used in the design in various research. However, far less investigations on their joint probability distribution have been carried out in the past.</p><p>In this study, the dataset of hourly surge height, and significant wave height of 89 TC events impacting along Hainan Island during 1949~2013 was obtained, which are simulated numerically with ADCIRC and SWAN respectively. Following that, 4 types of probability distributions for univariate were used to fit the marginal distribution of storm surge and wave. Secondly, Frank, Clayton and Gumbel Copula were tried to construct the joint probability distribution of wave and surge, and the optimal Copula was determined by K-S test and AIC, BIC criteria. Based on the optimal Copula selected for each area of interest, the joint return period of wave and surge was estimated.</p><p>The results show that, 1) the annual maximum value of the storm surge height and significant wave height of Hainan Island has a relatively obvious geographical distribution regularity. 2) GEV and Gumbel are the most optimal distribution for storm surge height and significant wave height respectively. 3) Clayton Copula is the best model for fitting joint probability of storm surge and wave. The estimated joining probability distribution can help the determination of design standard, and typical TC disaster scenario development.</p>

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

scholarly journals Analytical theory of turbulent diffusion

1961 ◽  
Vol 11 (2) ◽  
pp. 257-283 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Probability Distribution ◽  
Turbulent Diffusion ◽  
Similarity Theory ◽  
Probability Distributions ◽  
Joint Probability ◽  
Relative Displacement ◽  
Initial Position ◽  
Joint Probability Distribution ◽  
Variable Diffusion ◽  
High Reynolds

Recently Kraichnan (1959) has propounded a theory of homogeneous turbulence, based on a novel perturbation method, that leads to closed equations for the velocity covariance. In the present paper, this method is applied to the theory of turbulent diffusion and closed equations are derived for the probability distributions of the positions of marked fluid elements released in a turbulent flow.Two topics are discussed in detail. The first is the probability distribution, at timet, of the displacement of an element from its initial position. In homogeneous flows, this distribution is found to resemble that for classical diffusion but with a variable coefficient of diffusion which is proportional to$v^2_0 t$for$t \ll l|v_0$and which approaches a constant value [eDot ]lv0fortt[Gt ]l/v0(l= macroscale,v0= r.m.s. turbulent velocity).The second topic treated is the joint probability distribution of the displacements of two fluid elements. Particular attention is focused upon the probability distribution of relative displacement, i.e. Richardson's distance-neighbour function. This is found to be Gaussian for separationsrwhich are large ([Gt ]l). For smaller separations (r[Lt ]l), its behaviour at high Reynolds numbers is found to be quite well expressed in terms of a variable diffusion coefficientK(r,t), as suggested by Richardson (1926). For all but extremely short times,K(r,t) is found to depend only onrand on the form of the inertial range spectrumE(k). On assuming$E(r) \propto v^2_0 l(kl)^{- \frac {3}{2}}$as results from Kraichnan's approximation (1959), one finds$E(r) \propto v_0 l(r|l)^{ \frac {3}{2}}$. On the basis of similarity arguments of the Kolmogorov type, which give$E(r) \propto v^2_0 l(kl)^{- \frac {5}{2}}$, one finds$E(r) \propto v_0 l(r|l)^{ \frac {4}{3}}$as, in fact, Richardson originally proposed. The dispersionr2is proportional to$l^2(v_0 t|l)^4$on Kraichnan's theory; while$\langle r^2 \rangle \propto l^2 (v_0 t|l)^3$on the similarity theory. This illustrates that the behaviour of$\langle r^2 \rangle$is very sensitive to the spectrum.

scholarly journals Penerapan Metode Bayesian Network Model Untuk Menghitung Probabilitas Penyakit Sesak Nafas Bayi

2018 ◽  
Vol 2 (1) ◽  
pp. 62
Author(s):  
Hasniati Hasniati ◽  
Arianti Arianti ◽  
William Philip
Keyword(s):  
Probability Distribution ◽  
Bayesian Network ◽  
Conditional Probability ◽  
Network Model ◽  
Posterior Probability ◽  
Prior Probability ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Bayesian Network Model

Bayesian Network dapat digunakan untuk menghitung probabilitas dari kehadiran berbagai gejala penyakit. Dalam tulisan ini, penulis menerapkan bayesian network model untuk menghitung probabilitas penyakit sesak nafas pada bayi. Bayesian network diterapkan berdasar pada data yang diperoleh melalui wawancara kepada dokter spesialis anak yaitu data nama penyakit, penyebab, dan gejala penyakit sesak nafas pada bayi. Struktur Bayesian Network penyakit sesak nafas bayi dibuat berdasarkan ada tidaknya keterkaitan antara gejala terhadap penyakit sesak nafas. Untuk setiap gejala yang direpresentasikan pada struktur bayesian network mempunyai estimasi parameter yang didapat dari data yang telah ada atau pengetahuan dari dokter spesialis. Data estimasi ini disebut nilai prior probaility atau nilai kepercayaan dari gejala penyakit sesak nafas bayi. Setelah diketahui prior probability, langkah berikutnya adalah menentukan Conditional probability (peluang bersyarat) antara jenis penyakit sesak nafas dengan masing-masing gejalanya. Pada langkah akhir, nilai posterior probability dihitung dengan mengambil nilai hasil joint probability distribution (JPD) yang telah diperoleh, kemudian nilai inilah yang digunakan untuk menghitung probabilitas kemunculan suatu gejala. Dengan mengambil satu contoh kasus bahwa bayi memiliki gejala sesak, lemah, gelisah dan demam, disimpulkan bahwa bayi menderita penyakit sesak nafas Pneumoni Neonatal sebesar 0,1688812743.

CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

2018 ◽  
Vol 107 (3) ◽  
pp. 302-318
Author(s):  
JONATHAN BORWEIN ◽  
PHIL HOWLETT
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Marginal Distributions ◽  
Joint Probability Distributions

In modelling joint probability distributions it is often desirable to incorporate standard marginal distributions and match a set of key observed mixed moments. At the same time it may also be prudent to avoid additional unwarranted assumptions. The problem is to find the least ordered distribution that respects the prescribed constraints. In this paper we will construct a suitable joint probability distribution by finding the checkerboard copula of maximum entropy that allows us to incorporate the appropriate marginal distributions and match the nominated set of observed moments.

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