Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples
TLDR
In this paper, the mean and variance of normal populations from singly and doubly truncated samples having known truncation points are estimated with the aid of standard tables of areas and ordinates of the normal frequency function.Abstract:
This paper is concerned with the problem of estimating the mean and variance of normal populations from singly and doubly truncated samples having known truncation points. Maximum likelihood estimating equations are derived which, with the aid of standard tables of areas and ordinates of the normal frequency function, can be readily solved by simple iterative processes. Asymptotic variances and covariances of these estimates are obtained from the information matrices. Numerical examples are given which illustrate the practical application of these results. In Sections 3 to 8 inclusive, the following cases of doubly truncated samples are considered: I, number of unmeasured observations unknown; II, number of unmeasured observations in each `tail' known; and III, total number of unmeasured observations known, but not the number in each `tail'. In Section 9, singly truncated samples are treated as special cases of I and II above.read more
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References
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The Calculus of Observations.
Journal ArticleDOI
Maximum Likelihood Estimation of the Parameters of a Normal Distribution which is Truncated at a Known Point
TL;DR: In the first case, the observations form a random sample drawn from an incomplete normal distribution, but in the second case we sample from a complete normal distribution in which the obtainable information in a sense has been censored, either by nature or by ourselves.