The Analytical Estimator for Sparse Data

x x F x f y −∞ = ∫ dy Abstract—In parameter estimation of normal distribution, the conventional truncated normal estimator worked well only if the sample size is greater than 20. In this study, we consider to extend its usage for sparse data cases with sample size under 20. We derive a wide-sense truncated normal joint probability distribution function, composing of coverage, range, the sample of the first order, and data samples themselves, to analyze the problem of truncated normal distribution in sparse data estimation. We successfully improve the traditional truncated normal estimation by simply finding the solution from quadric polynomials without complex computations. Besides, we also shapes the formulations to guarantee the convergence of the population mean estimation if the standard deviation of population is known. u population mean σ standard deviation of population