Accession Number : AD0005410


Title :   SOME TWO SAMPLE TESTS BASED ON ORDERED OBSERVATIONS FROM THE EXPONENTIAL DISTRIBUTION


Corporate Author : WAYNE PUMP CO FORT WAYNE IN


Personal Author(s) : Epstein, Benjamin ; Tsao, Chia Kuei


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/005410.pdf


Report Date : 15 Dec 1952


Pagination or Media Count : 19


Abstract : 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 f(x; Asub1, theta sub 1) and f(x; Asub2, theta sub 2), respectively, where f(x; A, theta) = 1/theta exp (-(x-A)/theta). 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 g(x sub11,. ..,xsub1subrsub1; Asub1, theta sub1) and g(x sub21,...,x sub2sub4sub2; A sub2, thetasub2), where g(x sub1,x sub2,...,x subr; A,theta) = n'(n-r);1/theta to the power of r exp (- 1/theta(the sum of r i=1 (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. 1:94, 1936 and Ann. Eug., London 8:52, 1937). Similar likelihood ration tests based on S subrsub1 and S subrsub2 can be obtained by following Sukhatme's procedure. These likelihood ratios tests are reduced to equivalent tests which are expressed in terms of the well-known chi squared and Snedecor's 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.


Descriptors :   *POPULATION , *SAMPLING , *DISTRIBUTION FUNCTIONS , EXPONENTIAL FUNCTIONS , RANDOM VARIABLES , TEST AND EVALUATION , REDUCTION


Subject Categories : Statistics and Probability


Distribution Statement : APPROVED FOR PUBLIC RELEASE