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Statistical simulations with LR random fuzzy numbers
Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which...
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Random Numbers: The Backbone of Stochastic Simulations
I outlined the general process of simulation design in Chap. 8 . One topic I did not address applies to...
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Permanent Random Numbers, Poisson Sampling and Collocated Sampling
Permanent random numbers (PRN) sampling is a practical method to control sample overlap when samples are selected from the same sampling frame. In...
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Random Variables and Expectations
Random experiments have sample spaces may not consist of numbers. For instance, in a coin-tossing experiment, the sample space consists of the...
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Generating Random Numbers
To perform a Monte Carlo approximation, we have to generate random variables (rv.) on a computer according to a given df. F. In this chapter, we will...
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Many Random Variables
Concepts related to many random variables. The notion of independent and identically distributed random variables. Formulas related to many random...
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On the Baum–Katz theorem for randomly weighted sums of negatively associated random variables with general normalizing sequences and applications in some random design regression models
In this paper, we develop Jajte’s technique, which is used in the proof of strong laws of large numbers, to prove complete convergence for randomly...
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Continuous Random Variables
The definition of continuous random variables and their means and variances. An introduction to the normal distribution and the standardization...
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Functions of Random Variables
This chapter discusses single random variables and its transforms. Various types of transformations such as sum, squares, square-roots,...
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Functional strong law of large numbers for Betti numbers in the tail
The objective of this paper is to investigate the layered structure of topological complexity in the tail of a probability distribution. We establish...
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Random Matrix Time Series
In this paper, a time series model is proposed, where the coefficients take values from random matrix ensembles. Formal definitions, theoretical...
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Probability: One Discrete Random Variable
The definition of discrete random variables in probability theory. The definition of the probability distribution of a random variable and of...
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Four Finite Dimensional (FD) Surrogates for Continuous Random Processes
Numerical solutions of stochastic problems involve approximations of the random functions in their definitions by deterministic functions of time...
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A Random-Coefficients Analysis with a Multivariate Random-Coefficients Linear Model
Random-coefficients linear models can be considered as a particular case of linear mixed models. Different sources of variation are treated by random...
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Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications
In this paper, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of widely orthant dependent random variables...
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Random Vectors
We consider the concept and applications of random vectors in this chapter. In describing the probabilistic properties of a random vector, we need to...
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Normality test in random coefficient autoregressive models
In this paper, we consider the problem of testing for normality of the two unobservable random processes included in the first order random...
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Multiple Random Variables and Joint Distributions
Multiple r.v.s are often involved in various random experiments. For instance, an educator might examine the joint behavior of study time and grades,...
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An Interesting Class of Non-Kac Random Polynomials
As evident from classical results on random polynomials, it is difficult to derive the probability distribution of the number of real roots
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Approximated Gaussian Random Field Under Different Parameterizations for MCMC
Fitting spatial models with a Gaussian random field as spatial random effect poses computational challenges for Markov Chain Monte Carlo (MCMC)...