Finding a distribution to fit this curve

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If it is possible, could someone help me fit some kind of function to this curve? I thought a Lorentzian fit would work because of the peak and the tails, but it is causing problems. I will attach an image of the curve below. enter image description here Image of the general curve. The function used to fit the graph doesn't have to be perfect, but it should encompass the peak, with the right-hand tail included

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Maybe try fitting a curve of the form $$a \exp(-(x-b)^2) + c x + d$$