TY - JOUR

T1 - Central limit theorem for signed distributions1

AU - Hochberg, Kenneth J.

PY - 1980/6

Y1 - 1980/6

N2 - This paper contains an improved version of existing generalized central limit theorems for convergence of normalized sums of independent random variables distributed by a signed measure. It is shown that under reasonable conditions, the normalized sums converge in distribution to “higher-order” analogues of the standard normal random variable, in the sense that the density of the limiting signed distribution is the fundamental solution of a higher-order parabolic partial differential equation that is a generalization of the heat equation.

AB - This paper contains an improved version of existing generalized central limit theorems for convergence of normalized sums of independent random variables distributed by a signed measure. It is shown that under reasonable conditions, the normalized sums converge in distribution to “higher-order” analogues of the standard normal random variable, in the sense that the density of the limiting signed distribution is the fundamental solution of a higher-order parabolic partial differential equation that is a generalization of the heat equation.

KW - Central limit theorem

UR - http://www.scopus.com/inward/record.url?scp=84966245034&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1980-0565358-9

DO - 10.1090/S0002-9939-1980-0565358-9

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AN - SCOPUS:84966245034

SN - 0002-9939

VL - 79

SP - 298

EP - 302

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -