CONSTRUCTING A NEW WEIGHTED PROBABILITY DISTRIBUTION WITH APPLICATION

The weighted probability distributions are used when an investigator records an observation by nature according to a certain stochastic model. the recorded observation will not have the original distribution unless every observation is given an equal chance of begin recorded .A number of research using the concepts of weighted and size – biased sampling distribution due to importance of this kind of distribution and its application in many fields such as such as medicine, ecology, reliability and human populations. So we introduce this paper to explain one of double weighted distribution derived from inverse Weibull distribution using two types of weight functions. We work first on deriving the probability distribution and then to derive its cumulative distribution function and required moments of new weighted probability distribution. We provide a data analysis to see how the new model works in practice, the parameters and reliability function estimated using maximum likelihood method.