Analysis of medians under two-way model with and without interaction for Birnbaum-Saunders distributed response.

The Birnbaum-Saunders (BS) distribution, well-known as the fatigue-life distribution, has been used in numerous disciplines ranging from engineering to medical sciences. In this article, we develop a test for analysis of medians for BS distributed response to assess the impact of two interacting factors on the median, where no test is presently available. The proposed integrated likelihood ratio test (ILRT) eliminates the nuisance shape parameters by integrating them out. The second-order accurate asymptotic chi-square distribution of ILRT is derived. An in-depth simulation study strongly supports its excellent performance even under small group sizes. Furthermore, ILRT developed under the one-way model is found uniformly superior over its peers, is straightway extendable under general multiway setup, and has potential to be extended to other non-normal response variables. Its genuine need in industry, where non-normal responses are commonly encountered, is highlighted through analysis of three real data sets: ILRT strongly picked out the deposition time as influential factor in epitaxial layer experiment, revealed significant impact of spools on fiber life for the failure times of Kevlar 49 fiber data, and gave more accurate parameter estimates in delivery time data experiment, as assessed by various model adequacy tools, where its competitors failed to deliver desired results.

Two sample comparisons including zero-inflated continuous data: A parametric approach with applications to microarray experiment.

Micro-array experiments are important fields in molecular biology where zero values mixed with a continuous outcome are frequently encountered leading to a mixed distribution with a clump at zero. Comparison of two mixed populations, e.g. of a control and a treated group; of two groups with different types of cancer, to name a few, are often encountered in these contexts. Fairly skewed distribution of the continuous part coupled with small sample sizes are issues of main concern to be attended for the quality of inference in such situations while popularly used nonparametric methods rely on asymptotic distribution of the underlying test statistics which are valid only under large sample sizes. We address the aforementioned issues via a newly proposed exact test for location-scale family distributions and Generalized pivot quantity (GPQ) based parametric test procedures for non-location-scale distributions. Simulation based assessment showed their superior performance with respect to size and power in comparison to the popular two-part tests (Wilcoxon rank sum, t-test, Kolmogrov-Smirnov, Ansari-Bradley and Sigel-Tukey) more prominently for small sample sizes.

A new method for interval estimation of the mean of the Gamma distribution.

The two parameter Gamma distribution is widely used for modeling lifetime distributions in reliability theory. There is much literature on the inference on the individual parameters of the Gamma distribution, namely the shape parameter k and the scale parameter theta when the other parameter is known. However, usually the reliability professionals have a major interest in making statistical inference about the mean lifetime mu, which equals the product thetak for the Gamma distribution. The problem of inference on the mean mu when both parameters theta and k are unknown has been less attended in the literature for the Gamma distribution. In this paper we review the existing methods for interval estimation of mu. A comparative study in this paper indicates that the existing methods are either too approximate and yield less reliable confidence intervals or are computationally quite complicated and need advanced computing facilities. We propose a new simple method for interval estimation of the Gamma mean and compare its performance with the existing methods. The comparative study showed that the newly proposed computationally simple optimum power normal approximation method works best even for small sample sizes.