Weighted Distributions: A Brief Review, Perspective and Characterizations

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship between two truncated moments are presented

The Modified Double Weighted Exponential Distribution with Properties

The weighted distributions are widely used in many real life fields such as medicine, ecology, reliability, etc., for the development of proper statistical model. The concept of double weighted distribution was introduced by Al-khadim and Hantoosh (2013) and later has been studied by other researchers. In his article,  has been considered as suitable weight for efficient modeling of double weight exponential distribution. The statistical properties of the modified double weighted exponential distribution (MDWED) are explored. The Kolmogorov- Smirnov test has been used to choose a better fitted probability model. The result of this testshown that (MDWED) is more suitable distribution to fit rainfall data then (DWED) proposed by Al-khadim and Hantoosh (2013). Keywords:Weighted distribution, Exponential distribution, Moment Generating Function, Fisher information

The length-biased weighted exponentiated inverted Weibull distribution

Length-Biased distributions are a special case of the more general form known as weighted distributions. We can exploit the conceptuality of Length-Biased distribution in the development of appropriate models for lifetime data. Its method is adjusting the original probability density function from real data and the expectation of those data. This modification can lead to correct conclusions of the models. Therefore, we introduced the Length-Biased version of the weighted Exponentiated inverted Weibull distribution in this paper. Various properties and the expressions for moments, coefficient of skewness, coefficient of kurtosis, moment generating function, hazard rate function, etc. are derived. The maximum likelihood estimates of the parameters of the proposed distribution are determined. The study results suggest that this distribution is an efficacious model in life time data analysis and other related fields