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**Extra resources for Analytic Function Methods in Probability Theory: Colloquium Proceedings (Colloquia mathematica Societatis Janos Bolyai ; 21) **

**Example text**

Finally we give a negative answer to a question of P. FISCHER [6J.

G(x,t)1 S c 2 lit (i v) (v) for all x and 1 t, I xn S 7; nn tn with n>o,ntn 2n, for of ~ S 2 x and 2 with a positive number (independent t), ~ g(x,t) nxn S I ±, c3ntll ntn S (independent of x 2 ± and with a positive number t). - 32 - c3 PROOF. t]. 5) -exp (-II tIl 2 -2! t! i Then by n. 5) we get c 1 (n). 3. {A Let } +00 (r= 1 ,2, •.. ) n,r n=1 of probability measures on i 2 tending to positive integers lim sup k lim (i) r--+ oo n"'+ oo lim sup k lim (ii) r"'+ oo n"'+ oo lim sup k lim (iii) r"'+ oo for n"'+ oo a n - +00.

Knott, uber Inhalt, Springer, Berlin-Gottingen- 1957. The distribution of the Cramer-von Mises statistic for small sample sizes, J. , S. "- Ser. , 36(1974), Royal Stat. 430-438. Csorgo and L. Stacho Bolyai Inst. of Jozsef A. Aradi vertanuk tere I, University 6722 Szeged, Hungary - 65 - , COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 21. ANALYTIC FUNCTION METHODS IN PROBABILITY THEORY DEBRECEN (HUNGARY). 1977. NONNEGATIVE INFORMATION FUNCTIONS Z. DAR6CZY - GY. HAKSA I. INTRODUCTION The notion of information functions has been introduced by Z.