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A class of models indexed by two shape parameters is introduced, both to extend the scope of the standard logistic model to asymmetric probability curves and improve the fit in the noncentral probability regions. One-parameter subclasses can be used to examine symmetric or asymmetric deviations from the logistic model. The delta algorithm is adapted to obtain maximum likelihood estimates of the parameters. A review is made of other proposed generalizations. The standard linear logistic model is widely used for modeling the dependence of binary data on explanatory variables. Its success is due to its broad applicability, simplicity of form, and ease of interpretation. This model works well for many common applications; however, it assumes that the expected probability curve μ(η) is skew-symmetric about μ = ½ and that the shape of μ(η) is the cumulative distribution function of the logistic distribution. Symmetric …