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The Lorentzian distribution (aka Cauchy distribution) is a distribution function applicable to some physical phenomena including some types of spectral line broadening. The general form of the function (i.e., the Lorentzian function):
f(x) = a / (b+x²)
Like the normal distribution (and like the distribution of a rectangular component of velocity of the Maxwell-Boltzmann distribution), it has a curve with a bell-like (hill-like) shape (centered around a peak), but the shape differs from that of the normal distribution. It is applicable to two line-broadening mechanisms, natural broadening and pressure broadening.