Abstract
The Weibull distribution is a well known and common distribution. In this article, a skewness parameter to a Weibull distribution is introduced using an idea of Azzalini, which creates a new class of weighted Weibull distributions. This new distribution has a probability density function with skewness representing a general case of weighted probability density function of the Extreme value distribution, the Rayleigh distribution and Exponential distribution. Different properties of this new distribution are discussed and the inference of the old parameters and the skewness parameter is studied.
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