A non-uniform rate of convergence in a local limit theorem
1978 ◽
Vol 84
(2)
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pp. 351-359
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Keyword(s):
AbstractLet {Xn} be a sequence of iid random variables. If the common charac-teristic function is absolutely integrable in mth power for some integer m ≥ 1, then Zn = n−½(X1 + … + Xn) has a pdf fn for all n ≥ m. Here we give a necessary and sufficient condition for sup as n. → ∞, where φ (x) is the standard normal pdf and M(x) is a non-decreasing function of x ≥ 0 such that M(0) > 0 and M(x)/xδ is non-increasing for 0 < δ ≤ 1.
1980 ◽
Vol 03
(2)
◽
pp. 311-329
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Keyword(s):
1979 ◽
Vol 31
(2)
◽
pp. 255-263
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1983 ◽
Vol 27
(3)
◽
pp. 607-609
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1977 ◽
Vol 21
(2)
◽
pp. 384-385
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Keyword(s):
2013 ◽
Vol 50
(04)
◽
pp. 1206-1212
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1978 ◽
Vol 7
(1)
◽
pp. 101-111
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Keyword(s):
1980 ◽
Vol 87
(1)
◽
pp. 179-187
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