Abstract
Summary
The maximum likehood estimating equations are derived to estimate the mean and variance of a normal distribution from singly and doubly truncated samples of grouped observations with known truncation points, when the number of unmeasured observations is (1) unknown for each “truncated tail”, (2) known separately for each “trucated tail”, (3) known jointly for the two “truncated tails”. The equations are seen to be easily solvable with the aid of Gjeddebaek's (1949) tables of Z1 and Z2 functions. Asymptotic variance‐covariance matrix of the estimates is obtained in each of the three cases, and an investigation is made into the loss of information due to truncation of the samples. The corresponding results for the singly truncated samples are obtained as special cases of (1) and (2). Practical application of the results has been illustrated by a numerical example.
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