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.

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.

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.

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 The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang
Keyword(s):  
Probability Distribution ◽  
Law Of Large Numbers ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Degree Sequences ◽  
Strong Law ◽  
Large Numbers ◽  
Different Types ◽  
Azuma's Inequality ◽  
Growing Network

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

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