Small sample confidence intervals for the mean of a positively skewed distribution

Authors

Cherylyn Almonte, Florida International University

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

B. M. Golam Kibria

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Zhenmin Chen

Third Advisor's Name

Sneh Gulati

Fourth Advisor's Name

Dinesh Sharma

Date of Defense

7-9-2008

Abstract

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T₁ , T₃ and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T₁, mad T₁ , median T₃ and the mad T₃. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T₁ and median T₃ outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T₃ outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

Identifier

FI13101599

Recommended Citation

Almonte, Cherylyn, "Small sample confidence intervals for the mean of a positively skewed distribution" (2008). FIU Electronic Theses and Dissertations. 1074.
https://digitalcommons.fiu.edu/etd/1074