Accession Number:

AD0610770

Title:

ESTIMATION OF THE SCALE PARAMETER OF THE LOGNORMAL DISTRIBUTION BY M ORDER STATISTICS

Descriptive Note:

Master's thesis

Corporate Author:

AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

Personal Author(s):

• Highfield, Eugene R.

Report Date:

1964-08-01

Pagination or Media Count:

64.0

Abstract:

This thesis develops unbiased single order statistic and m-order- statistic estimators of the scale parameter of a truncated lognormal probability density function. In this development it is assumed that the location parameter is known and that if it is not zero, a transformed variable with a location parameter approximately zero can be obtained. The method of development of the singleorder-statistic estimator was to consider the expected value of the i-th order statistic. The development of the m-order-statistic estimator utilizes the development of the single-order-statistic estimator and then considers the variance of the m-order-statistic estimator as a Lagrangian function which is minimized to obtain the necessary weighting factors. These weighting factors are then combined with the other coefficients to obtain the desired multipliers. All the multipliers used to obtain the estimators, the variance of the estimators and their relative efficiencies are presented in tabular form as appendices.

Descriptors:

• *STATISTICAL FUNCTIONS
• DISTRIBUTION THEORY
• LEAST SQUARES METHOD
• PERMUTATIONS
• PROBABILITY
• STATISTICAL DISTRIBUTIONS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE