THE LENGTH-BIASED EXPONENTIATED INVERTED WEIBULL DISTRIBUTION

Abstract

This paper develops a length-biased of the exponentiated inverted Weibull (EIW) distribution, it is named as the length-biased exponentiated inverted Weibull (LBEIW).Some probability functions are derived, including the moments of this distribution.The length-biased inverted Weibull (LBIW) distribution is presented as a special case of the LBEIW distribution.Maximum likelihood estimation method is employed to parameter estimation.Finally, a real dataset of distance between cracks in a pipe is used to illustrate by fitting the LBEIW, EIW, LBIW and Weibull distributions to the data.It is shown that the LBEIW and EIW distributions can be fitted well.