Some properties of the bivariate lognormal distribution for reliability applications


Ramesh C. Gupta, Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, USA.



In this paper, we study the bivariate lognormal distribution from a reliability point of view. The conditional distribution of X given Y > y is found to be log-skew normal. The monotonicity of the hazard rates of the univariate as well as the conditional distributions is discussed. Clayton's association measure is obtained in terms of the hazard gradient, and its value in the case of our model is derived. The probability distributions, in the case of series and parallel systems, are derived, and the monotonicity of their failure rates is discussed. Three real applications of the bivariate lognormal distribution are provided, two from financial economics and one from reliability. Copyright © 2012 John Wiley & Sons, Ltd.