STATISTICAL TESTS INVOLVING SEVERAL INDEPENDENT GAMMA DISTRIBUTIONS

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

1Division of Mathematics, Computer Science and Statistics, University of Texas, San Antonio, TX 78249, U.S.A. 2Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, U.S.A. 3IBM 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.