SOME TWO SAMPLE TESTS BASED ON ORDERED OBSERVATIONS FROM THE EXPONENTIAL DISTRIBUTION
WAYNE PUMP CO FORT WAYNE IN
Pagination or Media Count:
Two random samples, S sub n1 and S sub n2 xsub11 or xsub12 or ... or x sub 1n1 and x sub 21 or x sub 22 or ... or x sub2 sub n2, are considered from populations having p.d.f.s fx Asub1, theta sub 1 and fx Asub2, theta sub 2, respectively, where fx A, theta 1theta exp -x-Atheta. S subrsub1 and S subrsub2 are assumed to be the sets of the first r sub1 and r sub2 smallest observations of S subnsub1 and S subnsub2, respectively. The p.d.f.s of S subrsub1 and S subrsub2 are given by gx sub11,. ..,xsub1subrsub1 Asub1, theta sub1 and gx sub21,...,x sub2sub4sub2 A sub2, thetasub2, where gx sub1,x sub2,...,x subr A,theta nn-r1theta to the power of r exp - 1thetathe sum of r i1 x sub i-A n-r x subr - A. The likelihood ratio tests based on the complete sets S subnsub1 and S subnsub2 are special cases of those obtained by Sukhatme Stat. Res. Mem. 194, 1936 and Ann. Eug., London 852, 1937. Similar likelihood ration tests based on S subrsub1 and S subrsub2 can be obtained by following Sukhatmes procedure. These likelihood ratios tests are reduced to equivalent tests which are expressed in terms of the well-known chi squared and Snedecors F distributions. Some of the tests can be extended to k-sample tests. Since percentage points for the chi squared and F distributions are tabled, tests involving these random variables are useful in applications.
- Statistics and Probability