Confidence Interval for the Ratio of Lognormal Means When the Coefficients of Variation are Known
Sa-aat Niwitpong · International Journal of Mathematics Trends and Technology · 2015
This paper presents the confidence interval for the ratio of means of lognormal distribution. We derived analytic expressions to find the coverage probability and the expected length of the proposed confidence interval. The lognormal distribution has been widely used for a skewed data in science, biology and economics. A ratio estimator is much attention in area of bioassay and bioequivalence. Recently, many researchers have been investigated this problem. For example, Lee and Lin (3) constructed the confidence interval for the normal means by using the generalized confidence interval and the generalized p-value proposed by (6). Later, Chen and Zhou (2) compared several methods for constructing the confidence interval for the ratio of lognormal means. They suggested a modified signed log-likelihood ratio approach which is the best among these confidence intervals. In this paper, we proposed to construct the confidence interval for the lognormal means when the coefficients of variation are known. Additionally, we derived analytic expressions to find its coverage probability and its expected length. Let 1 2 , ,..., , 1, 2, i i i i n X X X X i