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

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** Department of Statistics Department of Mathematics **

** Panjab University Guru
Nanak Dev University **

**Chandigarh-160014 Amritsar-143005 **

**India.
India.**

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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., F_{i}(.) 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 X_{i:r+1 }and X_{i: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 H_{0}
for large values of W_{r}. 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 W_{r}. 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**.**