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rejected

Test at a 5% significance level, the critical value is 5.991465

0.0754 0.963002 not rejected

APPENDIX B: PROOFS

B.1 Positivity conditions theorem (Theorem 1)

Let us consider a Gaussian Gram-Charlier expansion of order 4 with our usual notation:

/(s) —-u e— 1 (-')2 f 1 — (3^ — (s—jm)M^ (5.27)

We know that:

1 1 2 — e-1 (s-m) > 0 V(m, a, s) e R x R+x R aV2^

since it is a probability density function. To have /(s) - s(s) > 0 Vs e R we need to verify that:

Which is equivalent to:

0 0

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