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Factions in Morris' natural exponential quadratic variance family and a lack of consensus in sample size determination

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  • Shanmugam, Ramalingam

Abstract

Morris (1982, 1983) shows that there exists only six distributions with variance as a quadratic function of the mean, and calls the group natural exponential-quadratic variance family (NEQVF). This note discovers that in NEQVF there are actually two factions which we call linear and nonlinear mean exponential families (MEF and NLMEF). A statistical utility of this characterization lies in determining a sample size based on Shannon's information criterion: As far as gathering information with respect to the population mean, there is a consensus formula in NEQVF for sample size determination, but with respect to the natural parameter, there are three opinions -- one for LMEF and a different one for each member of NLMEF.

Suggested Citation

  • Shanmugam, Ramalingam, 1992. "Factions in Morris' natural exponential quadratic variance family and a lack of consensus in sample size determination," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 117-120, September.
    • Handle: RePEc:eee:stapro:v:15:y:1992:i:2:p:117-120
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