الفهرس 
A new family of distributions related to weibull distribution
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Abstract
In recent years, statistical distributions are commonly applied to describe real world phenomena. Due to the usefulness of statistical distributions, their theory is widely studied and new distributions are developed. The interest in developing more flexible statistical distributions remains strong in statistics. Many generalized classes of distributions have been developed and applied to describe various phenomena. A common feature of these generalized distributions is that they have more parameters. In this thesis, a new four-parameter lifetime distribution, called Weibull quasi Lindley has been introduced. This distribution is a particular case from Weibull{u2013}G family which previously introduced by Bourguignon et al. (2014). Its density function is very flexible and can be symmetrical, left-skewed and right-skewed. It has constant, increasing, decreasing and bathtub shaped hazard rate function. Various structural properties are derived including explicit expressions for the quantile function. Also explicit expressions for the Rényi and q-entropies are derived. The order statistics of the probability distribution is derived. Additionally the maximum likelihood method is used to estimate the model parameters and the potentiality of the new model is illustrated by means of three applications to real data. In other hand, two new generated families of probability distributions are introduced depending on the additive Weibull distribution as a generator. The first new generated family of distributions called the additive Weibull generated family (AW-G family). The AW-G family is defined by using the AW as a generator instead of the Weibull generator in the Weibull-G family. Some special models of the family are presented and some mathematical properties are provided. Also, the estimation of the model parameters is performed by the method of maximum likelihood, furthermore two illustrative applications based on real data are investigated