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 -