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Small Sample Properties of Asymptotically Efficient Estimators of the Parameters of a Bivariate Gaussian–Weibull Distribution



Publication type:

Research Paper (RP)

Primary Station(s):

Forest Products Laboratory


USDA Forest Service, Forest Products Laboratory, Research Paper, FPL-RP-667, 2012: 48 p.


Two important wood properties are stiffness (modulus of elasticity or MOE) and bending strength (modulus of rupture or MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two or three parameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood system reliability calculations, in a 2012 paper Verrill, Evans, Kretschmann, and Hatfield introduced a bivariate Gaussian–Weibull distribution and the associated pseudo-truncated Weibull. In that paper, they obtained asymptotically efficient estimators of the parameter vector of the bivariate Gaussian–Weibull. In this paper, we discuss computer simulations that investigated the small sample properties of these parameter estimates. We also discuss a Web-based computer program that obtains these estimates.


Verrill, Steve P.; Evans, James W.; Kretschmann, David E.; Hatfield, Cherilyn A. 2012. Small sample properties of asymptotically efficient estimators of the parameters of a bivariate Gaussian–Weibull distribution. Research Paper FPL-RP-667. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 46 p.


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