The algebra of random variables

By P. R. Nelson. 1979

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Many well-established frameworks for arithmetic operations on independent random variables involve integral transform methods such as Fourier and Mellin transforms (Springer 1979) which only allow for some simple cases, e.g., the sum, difference, product, or quotient of independent random variables.”
A new baseline model for estimating willingness to pay from discrete choice models (2013, background): “Typical algebraic operations on multivariate random variables result in sum distributions, difference distributions, product distributions, and ratio (or quotient) distributions (Springer, 1979).”
Performance Analysis of Free-Space Optical Links Over Málaga ($\mathcal{M} $) Turbulence Channels With Pointing Errors (2018, unknown): “2) Asymptotic Analysis: Using [31, Eq.”
Dependence in Dempster-Shafer theory and probability bounds analysis* (2004, methodology): “The algorithms of Yager (1986), Williamson (1989; Williamson and Downs 1990) and Berleant (1993; 1996; Berleant and Goodman-Strauss 1998) provide bounds for convolutions (i) under an assumption of independence, and (ii) in the Fréchet case with no assumption at all about dependence between the varia”
Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models (2008, methodology): “To date, only a few authors (e.g., Bollen, 1987, 1989; Brown, 1997; Cheung, 2007; MacKinnon, 2000; West & Aiken, 1997) have devoted attention to the simultaneous testing of multiple indirect effects, yet the potential uses for such methods are clear and abundant.”
A Value Function for Assessing Sustainability: Application to Industrial Buildings (2010, methodology): “Other approaches include using probability density functions [16], optimization methods [1], interactive methods [17], and fractals [1], which require the decision maker to have a clear idea of values, the degree of precision required at the moment of evaluation, and the probability of the phenomeno”
Contemporary approaches to assessing mediation in communication research. (2008, background): “, 2004) circumvents the need to assume normality by making use of the known distribution of the product of two normally distributed variables (Aroian, 1947; Craig, 1936; MacKinnon et al., 2004; Springer, 1979).”
Marginal distributions of sequential and generalized order statistics (2003, background): “In case of ordinary order statistics, the result is given in Blom (1958, p. 68) and Arnold and Balakrishnan (1989, p. 58).”
PaCAL: A Python Package for Arithmetic Computations with Random Variables (2014, methodology): “For example one of the solutions to the Behrens-Fisher uses the statistic t 1 sin θ − t 2 cos θ for some constant θ (Springer 1979).”