Transitive Methods

2019 ◽  
pp. 9-44
Author(s):  
Georges Matheron
Keyword(s):  
Numerical Computation ◽  
Random Variable ◽  
Indicator Function ◽  
Isotropic Case ◽  
Estimation Variance ◽  
Regular Grid ◽  
Numerical Function ◽  
Transition Phenomenon ◽  
Simple Rules

Chapter 2, devoted to deterministic transitive methods, introduces the notion of a transition phenomenon by using the example of the indicator function of a set, which is described by means of its geometrical covariogram. This notion is then extended to any numerical function f of the space. The next step consists in studying in detail the operation of ‘grading’ in the isotropic case, where the initial pointwise regionalised variable is replaced by its regularised average along a line, as would occur during drilling. Simple rules for passing from the pointwise covariogram to the graded one are given. When the regionalised variable is recognised by a regular grid whose origin has a random setting, the integral of function f becomes a random variable. Its estimation variance is expressed in terms of the covariogram, and the rules about regularisation allow the numerical computation of this variance. The case of set indicators is treated in detail.

A PÓLYA LATTICE MODEL TO STUDY LEVERAGE DYNAMICS AND CONTAGIOUS FINANCIAL FRAGILITY

2012 ◽  
Vol 15 (supp02) ◽  
pp. 1250069 ◽  
Author(s):  
PASQUALE CIRILLO ◽  
MAURO GALLEGATI ◽  
JÜRG HÜSLER
Keyword(s):  
Business Cycles ◽  
Lattice Model ◽  
Balance Sheet ◽  
Random Variable ◽  
Financial Fragility ◽  
Economic Wealth ◽  
Industrial Economy ◽  
Simple Rules ◽  
Approaches To Study ◽  
Leverage Dynamics

We discuss a special Pólya lattice model to study cascading failures of firms in a simple industrial economy. In particular, every firm is represented by a Pólya-like urn, whose reinforcement is function of time, of the neighboring urns and their compositions, and of a random variable representing systemic risk or fate. The simple idea is to build the dependence among firms by assuming simple balance sheet rules on debts and credits. In detail we assume that the debts of every company are credits for some of its neighbors. Debts and credits are represented by different balls in the urns/firms. At the same time we assume that the riskiness of every firm also depends on the economic wealth of its neighbors and of the economy in general. These simple rules are sufficient to create business cycles, in which the accumulation of debts pushes the economy towards frequent crises. The model can be easily simulated and the results we obtain encourage the development of brand new finitary probabilistic approaches to study firms' behavior and dynamics.

scholarly journals Numerical Computation of the Small Balls Probability for RandomFunctions with Normal Components

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Data Analysis ◽  
Characteristic Function ◽  
Numerical Computation ◽  
Statistical Methods ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Random Variables ◽  
Random Variable ◽  
Random Functions

Statistical methods are often based on the properties of the distribution of random variables or randomvectors. In functional data analysis (FDA) we do not work with random observation containing a finite randomvector, but the whole function is one observation. We call it the functional random variable or the randomfunction, in short. This paper offers the possibility to generate random functions with normal components. In thiscase, the probability of small balls can be calculated numerically using the characteristic function. This tool canbe very useful in simulations and testing various kinds of estimates.

Imagine Law Without Simple Rules

1995 ◽  
Vol 40 (2) ◽  
pp. 143-144
Author(s):  
Arthur C. Graesser
Keyword(s):  
Simple Rules

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Soil Spatial Heterogeneity and Systems of Agriculture

2015 ◽  
Vol 2 (1) ◽  
pp. 50-59
Author(s):  
V. Medvedev
Keyword(s):  
Spatial Heterogeneity ◽  
Soil Cover ◽  
Regular Grid ◽  
Resource Saving ◽  
The Third ◽  
Soil Spatial Heterogeneity ◽  
Agriculture Systems ◽  
Zonal Soils

Aim. To consider soil continuality and discreteness as features of heterogeneity manifestation in a soil cover, important for construction of agriculture systems. Methods. Geostatistical research of soil spatial heterogeneity, revealing the contours of a fi eld with various parameters of fertility. Results. The use of principles of precise agriculture and inspection of indicative properties of fi eld soils using a regular grid allowed to divide a fi eld into contours with three levels of fertility: the fi rst one is characterized by optimal or close to optimum properties which allows refusing from (or reducing substantially) tillage, introduction of fertilizers or chemical ameliorates; the second one has average parameters of fertility corresponding to zonal soils and demands the application of zonal technologies; the third one (with the worst parameters of fertility) presupposes regular use of the improved technologies. Conclusions. The introduction of precise agriculture will allow replacing a traditional zonal system with thenew which is soil-protecting and resource-saving one.

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