I am looking for a monotonically decreasing function to fit a cumulative distribution. The distribution is the number of values of a random variable X, that are greater than Y as a function of Y. In total, there are a few hundred values of X so the distribution does not decrease smoothly. I am thinking of fitting it with a monotonically decreasing polynomial to obtain a smoothly decreasing function of Y. I would like to choose the degree of the polynomial to get a satisfactory fit. Can someone suggest a monotonically decreasing polynomial to use.
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