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Solutions to some functional equations and their applications to characterization of probability distributions
C. G. Khatri,C. Radhakrishna Rao +1 more
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In this paper, the authors consider two sets of functions Li9, Lq and Mlf, Mp of independent random variables Xl9 Xn with the condition that the unknown functions in these two types of equations are polynomials of an assigned degree.Abstract:
involving an unknown function ?5 of a single variable t Conditions under which the unknown functions in these two types of equations are polynomials of an assigned degree are given The third, on the characterization of normal and gamma distributions, extends the earlier work of the authors (Rao, 1967 and Khatri and Rao, 1968*) We consider two sets of functions Li9 , Lq and Mlf , Mp of independent random variables Xl9 Xn with the conditionread more
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References
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Characterisation of the distribution of random variables in linear structural relations
TL;DR: In this paper, the authors examined the nature of the latent random variables which occur in linear structural models, under the assumption that they are independent and showed that alternative representations with different sets of coefficients for the latent variables or different numbers of latent variables are possible when and only when some of the variables or some of their linear combinations have a univariate normal distribution.
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