Asymptotic homogeneity tests for mean exponential family distributions.

*(English)*Zbl 0677.62011Summary: A new class of distributions is defined, called the Mean Exponential Family (MEF). An asymptotic test statistic is derived to examine the homogeneity of a sample from the MEF, and then, expressions are obtained for binomial, Poisson, negative binomial, beta, gamma, normal, Pareto, Laplace, and Rayleigh distributions as special cases. As the results confirm a known underlying distribution for many data in the literature, there are advantages in the presented approach.

##### MSC:

62E10 | Characterization and structure theory of statistical distributions |

62F03 | Parametric hypothesis testing |

##### Keywords:

Morris’ natural exponential quadratic variance family distributions; characterization; statistical power; Mean Exponential Family; asymptotic test statistic; MEF; binomial; Poisson; negative binomial; beta; gamma; normal; Pareto; Laplace; Rayleigh distributions
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\textit{R. Shanmugam}, J. Stat. Plann. Inference 23, No. 2, 227--241 (1989; Zbl 0677.62011)

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##### References:

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