| H. Cramer, Random Variables and Probability Distributions, 3rd edition, Cambridge University Press, London, 1970. |
....Q(a) 51) Q(a) 52) Q(a) a 2 # i T i 1 (a) 53) This results in a closed form expression for computing probability of error. 13 VII. CONVERGENCE PROPERTIES Convergence properties of Gram Charlier expansion is investigated in [24] 29] [30]. It is proved in [31] that the expansion is convergent if the expanded function satisfies the following condition, f Y (y)e 4 dy #. 54) Reference [13] mentions that this expansion has good asymptotic behavior as defined in [32] In other words, a few terms will give a close ....
H. Cramer, Random Variables and Probability Distributions, 3rd edition, Cambridge University Press, London, 1970.
....a 2 R 1 fi fi gn (t; a) fi fi c 1 Gamma n GammaA jfftj Gamma1= m2 m ) Delta (1) provided that c 2 jfftj n (m Gamma1) 2 Gamma : 2) Remark. If X has a discrete distribution it is well known that gn (t; a) is an almost periodic function (see e.g. Besicovitch (1932) p. 6, and Cramer (1970), p.26) and hence lim t 1 fi fi gn (t; a) fi fi = 1: Thus, jtj has to be restricted to a finite interval depending on n and f . The aim of this paper is to show that in (1) the exponent 1= m2 m ) of jtj Gamma1 can be replaced by a larger value in the following two cases: a) the ....
Cramer H., "Random variables and probability distribution," Cambridge, 1970.
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H. Cramer, Random Variables and Probability Distributions, 3rd edition, Cambridge University Press, London, 1970.
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Cramer, H. (1937), Random Variables and Probability Distributions. Cambridge, U.K.: Cambridge Tracts.
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