Mathematical Researches

Failure rate is one of the important concepts in reliability theory. In this paper, we introduce a new distribution function containing four parameters based on inverse Weibull distribution. This new distribution has a more general form of failure rate function. It is able to model five ageing classes of life distributions with appropriate choice of parameter values so that it is displayed decreasing, increasing, bathtub shaped, unimodal and increasing-decreasing increasing  failure rates and the new distribution has also a bimodal density function.  The moments, the order statistics, reliability parameters are obtained. The method of maximum likelihood is used to estimate the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the advantage of the proposed distribution.