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Statisticians sample data and try to estimate the underlying distribution from which the data came. Can anything be done when the sample size is small (~ 5)? In this work, directed by Roger Wets with Michael Casey, we posed the estimation question as a constrained optimization problem. In this framework, we are able to exploit information we may have about the distribution in addition to the 5 data points, e.g., continuity, modality, monotonicity, etc. The resulting estimates appear to outperform standard methods; we have been experimenting with Fourier and wavelet basis functions.