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STATISTICAL TESTS INVOLVING SEVERAL INDEPENDENT

GAMMA DISTRIBUTIONS

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RAM C. TRIPATHI^{1}, RAMESH C. GUPTA^{2} AND ROBERT K. PAIR^{3}

^{1} *Division of Mathematics, Computer Science and Statistics,*

University of Texas, San Antonio, TX 78249, U.S.A.

^{2} *Department of Mathematics and Statistics, University of Maine,*

Orono, ME 04469-5752, U.S.A.

^{3} *IBM Federal Systems Co., Houston, TX 77058, U.S.A.*
(Received February 26, 1992; revised October 12, 1992)

**Abstract.**
Statistical tests are developed regarding linear
combinations of the parameters of several independent gamma populations.
The tests are based on a generalized minimum chi-square procedure. On
utilizing these, one can test hypotheses regarding the means or the scale
parameters when the shape parameters are unknown. In these tests there is
no need to assume the equality of the shape parameters of the underlying
populations. Tests for comparing coefficients of variation of several
gamma populations have also been developed. For the two population case, a
power comparison of these tests with some existing tests is also
presented. Two examples are provided to explain the procedure.

*Key words and phrases*:
Gamma distribution, test of
hypotheses, scale parameters, coefficient of variation, minimum
chi-square, power of a test, test statistic.

**Source**
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