The paper deals with reciprocals of positively truncated normal random variables. E. C. Grab et I. R. Savage (1954) studied E [1/
X] for the positive Bernoulli and positive Poisson variable
X. Correspondingly, this paper considers “positive normal variable
X”, that is,
X is the normal variable such that μ=E[
X] is so large compared with σ
2=
V[
X] that the range of
X is effectively positive. Our main result is as follows: for a positive normal variable
X with parameters μ and σ
2,
E[1/
Xm]=(1/α
m){1+
m(
m+1)σ
2/2α
2}
approximately hold for positive integers
m if α/σ is large.
抄録全体を表示