Weibull and inverse Weibull composite distribution for modeling reliability data

The Weibull distribution, frequently used for life data analysis, is composited with inverse Weibull distribution to obtain a computationally convenient parametric distribution for modeling reliability data. This two-parameter smooth and continuous natural composition has an inverse Weibull density up to an unknown threshold value and Weibull density for the remainder. The resulting density is similar in shape to the inverse Weibull density, yet its upper tail is lighter than the Weibull density. And, the right-tail behavior is quite similar to the Weibull density. The least squares parameter estimation technique is discussed by analyzing a repair time reliability data.