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In this paper, a new method is proposed for generating families of continuous distributions. A random variable X , "the transformer", is used to transform another random variable T , "the transformed". The resulting family, the T -X family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable X . Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions.

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Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-andneck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.

The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of distributions. This paper proposes the use of quantile functions to define the W function. Some general properties of this T-X system of distributions are studied. It is shown that several existing methods of generating univariate continuous distributions can be derived using this T-X system. Three new distributions of the T-X family are derived, namely, the normal-Weibull based on the quantile of Cauchy distribution, normal-Weibull based on the quantile of logistic distribution, and Weibull-uniform based on the quantile of log-logistic distribution. Two real data sets are applied to illustrate the flexibility of the distributions.

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