def fractions_discrete(self, ds, n=None):
        r'''Computes the fractions of the cumulative distribution functions 
        which lie between the specified specified particle diameters. The first
        diameter contains the cdf from 0 to it. 
        
        Parameters
        ----------
        ds : list[float]
            Particle size diameters, [m]
        n : int, optional
            None (for the `order` specified when the distribution was created),
            0 (number), 1 (length), 2 (area), 3 (volume/mass),
            or any integer, [-]

        Returns
        -------
        fractions : float
            The differences in the cumulative distribution functions at the 
            specified diameters and order, [-]
        
        Examples
        --------
        >>> psd = PSDLognormal(s=0.5, d_characteristic=5E-6, order=3)
        >>> psd.fractions_discrete([1e-6, 1e-5, 1e-4, 1e-3])
        [0.0006434710129138987, 0.9165280099853876, 0.08282851796190027, 1.039798247504109e-09]
        '''
        cdfs = [self.cdf(d, n=n) for d in ds]
        return [cdfs[0]] + diff(cdfs)