There has been growing in study of reliability in subjects such as survival function, failure (reversed failure) rate and their properties. Generalized failure (reversed failure) rate have useful applications in economics, for example supply chain contractor and pricing. Based on Lariviere and Porteus p2001q, Lariviere p2006q and Torrado and Oliveira p2013q, various notes on generalized failure (reversed failure) rate and elasticity functions are derived. Also characteristic of increasing generalized failure (reversed failure) rate and their properties achieved in view of elasticity functions. Lorenz curves have important role in inequality measure studying and many extensions are discussed up to now. We have concentrated on aspects of Lorenz curves and their connection with elasticity of Lorenz curves, distorted Lorenz curve and extended version of distorted Lorenz curve.

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