Type of Document Master's Thesis Author Hayles, George Carlton URN etd-10302008-120613 Title Variances of some truncated distributions for various points of truncation. Degree Master of Science Department Statistics Advisory Committee

Advisor Name Title Jensen, Donald R. Committee Chair Harshbarger, Boyd Committee Member Pickands, James J. III Committee Member Keywords

- Analysis of variance
Date of Defense 1966-12-06 Availability unrestricted AbstractThe purpose of this study is to examine variances in the case of distributions obtained by truncating a given distribution at various points. In particular, the truncated distributions are restricted to nested increasing intervals, and the question is posed whether the variances of these distributions are monotonically increasing. The answer to this question is relevant to the use of conditional information for purposes of estimation and prediction.Several tables are presented in the thesis which provide evidence of the property of monotonic variance for nested increasing intervals of truncation in the case of univariate distributions., The Monte Carlo procedure is used to determine a table of standard deviations for the standard normal distribution with the same points of truncation reported by Clark(2). Clark's table is given intact, and it is used in comparison with the new table reported here as a check on the Monte Carlo procedure used in the present study.

Distributions other than the standard normal distribution are examined as well, namely, a Pearson U-shaped distribution and a bimodal distribution consisting of a mixture or two Pearson distributions. Graphs of the U-shaped and bimodal distributions are given.

A section is given in which dispersion for a bivariate case is examined in terms of the bivariate normal distribution. An interesting trend among the covariance matrices is observed in the data reported in that section.

A separate computer program for each type of distribution was written and used to calculate the variances of the truncated distributions. FORTRAN programs and flow charts are presented in the Appendix. Explanation of the tables and procedures used to calculate the entries in the body of each table are given in each section as well as some discussion of the results presented.

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