Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution

This paper introduces a transmuted modified Weibull distribution as an important competitive model which contains eleven life time distributions as special cases. We generalized the three parameter modified Weibull distribution using the quadratic rank transmutation map studied by Shaw et al. [12] to develop a transmuted modified Weibull distribution. The properties of the transmuted modified Weibull distribution are discussed. Least square estimation is used to evaluate the parameters. Explicit expressions are derived for the quantiles. We derive the moments and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. This model is capable of modeling of various shapes of aging and failure criteria.