SAMPLE QUASI RANGES BASED CLASS OF ONE SIDED TESTS AND RELATED MULTIPLE COMPARISONS

 

 

Amar Nath Gill Parminder Singh

Department of Statistics Department of Mathematics

Panjab University Guru Nanak Dev University

Chandigarh-160014 Amritsar-143005

India. India.

ABSTRACT

 

 

Let the data from the ith treatment/population follow a distribution with cumulative distribution function (cdf) Here is the location (scale) parameter and F(.) is any absolutely continuous cdf, i.e., Fi(.) is a member of location-scale family, i=1,,k. In this paper we propose a class of tests to test the null hypothesis against the simple ordered alternative with at least one strict inequality. In literature use of sample quasi range as a measure of dispersion has been advocated for small sample size or sample contaminated by outliers (see David (1981) section 7.4).

 

Let be a random sample of size n from the population be the sample quasi range corresponding to this random sample, i=1,,k. Here Xi:r+1 and Xi:n-r represent (r+1)th and (n-r)th order statistics and [x] represents the greatest integer contained in x . The proposed class of tests, for the general location scale setup, is based on the statistic The test is reject H0 for large values of Wr. The construction of a three-decision procedure and simultaneous one-sided lower confidence bounds for the ratios, , have also been discussed with the help of the critical constants of the test statistic Wr. Applications of the class of tests to uniform and two parameter exponential probability models have been discussed separately with necessary tables and comparison of some members of our class with the test of Gill and Dhawan (1999) in terms of simulated power, is presented under exponential probability model.

 

 

Key Words : Quasi range; Ordered alternative; Critical point; Simultaneous confidence bounds; Misclassification; Type III-error.