Find Mean Residual Life of a bounded variable











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Define



$$Sleft( xright) = 1- exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



Let



$$fleft( xright) =frac{alpha beta}{x^{beta-1}} exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



I want to evaluate the following integral:



$$mleft( tright) =frac{int_{t}^{1}ufleft( uright) }{Sleft( tright)}-t $$






integration







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    up vote
    0
    down vote

    favorite












    Define



    $$Sleft( xright) = 1- exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



    Let



    $$fleft( xright) =frac{alpha beta}{x^{beta-1}} exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



    I want to evaluate the following integral:



    $$mleft( tright) =frac{int_{t}^{1}ufleft( uright) }{Sleft( tright)}-t $$






    integration







    share|cite|improve this question


























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Define



      $$Sleft( xright) = 1- exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



      Let



      $$fleft( xright) =frac{alpha beta}{x^{beta-1}} exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



      I want to evaluate the following integral:



      $$mleft( tright) =frac{int_{t}^{1}ufleft( uright) }{Sleft( tright)}-t $$






      integration







      share|cite|improve this question















      Define



      $$Sleft( xright) = 1- exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



      Let



      $$fleft( xright) =frac{alpha beta}{x^{beta-1}} exp left[ -alphaleft( x^{-beta}-1right) right], 0<x<1; alpha>0; beta>0$$



      I want to evaluate the following integral:



      $$mleft( tright) =frac{int_{t}^{1}ufleft( uright) }{Sleft( tright)}-t $$






      integration




      integration






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 23 hours ago









      KM101

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