On Estimating the Mean and Standard Deviation of Truncated Normal Distributions

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Abstract
The problem considered is that of estimating the mean and standard deviation of a normally distributed population from a truncated sample when neither count nor measurements of variates in the omitted portion of the sample is known. Formulas are developed whereby certain special functions required-in solutions given for this problem by Karl Pearson and Alice Lee and by R. A. Fisher may be readily evaluated with the aid of an ordinary table of the areas and ordinates of the normal curve. A method of successive approximations is illustrated which, with the aid of the above formulas permits the utilization of either the Pearson-Lee or the equivalent Fisher method to obtain the desired estimates with an improvement in accuracy regardless of whether or not the special tables ordinarily required by these two methods are available.

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