= J. Gil-Pelaez
{c}
<J. Gil-Pelaez> authored the 1951 <Note on the inversion theorem by J. Gil-Pelaez>, giving a way to recover a distribution function from its <characteristic function>. The primary journal byline supplies the verified initials.<Note on the inversion theorem by J. Gil-Pelaez>[Biometrika 38, pp. 481–482]{ref}
The inversion integrates an oscillatory expression involving the characteristic function. At a discontinuity, the formula naturally returns the midpoint of the two one-sided distribution values. Keeping this convention explicit matters for discrete laws as well as continuous ones: an inversion formula is not automatically a pointwise identity at every jump.<Note on the inversion theorem by J. Gil-Pelaez>[Inversion identity, pp. 481–482]{ref}
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