distribution of $X=(e^Y-1)^1/theta$ where Y is exponential distributed

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Let $Y sim textExp(lambda)$ what's the NAME of the distribution of X such that

$$X equiv (e^Y -1)^1/theta$$ where $theta$ is a positive constant.




probability-theory random-variables




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    up vote
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    Let $Y sim textExp(lambda)$ what's the NAME of the distribution of X such that

    $$X equiv (e^Y -1)^1/theta$$ where $theta$ is a positive constant.




    probability-theory random-variables




    share|cite|improve this question























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Let $Y sim textExp(lambda)$ what's the NAME of the distribution of X such that

      $$X equiv (e^Y -1)^1/theta$$ where $theta$ is a positive constant.




      probability-theory random-variables




      share|cite|improve this question













      Let $Y sim textExp(lambda)$ what's the NAME of the distribution of X such that

      $$X equiv (e^Y -1)^1/theta$$ where $theta$ is a positive constant.





      probability-theory random-variables





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      share|cite|improve this question




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      edited Aug 1 at 17:41









      Dzoooks

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      asked Aug 1 at 17:18









      Agustín Cugno

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          You can show that the random variable X obeys the CDF



          $F_X(x)=1-frac1(1+x^theta)^lambda$ , $xin[0,infty)$



          which can subsequently be classified as a Pareto type IV with $mu=0$ and $sigma=1$.






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            up vote
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            You can show that the random variable X obeys the CDF



            $F_X(x)=1-frac1(1+x^theta)^lambda$ , $xin[0,infty)$



            which can subsequently be classified as a Pareto type IV with $mu=0$ and $sigma=1$.






            share|cite|improve this answer

























              up vote
              2
              down vote













              You can show that the random variable X obeys the CDF



              $F_X(x)=1-frac1(1+x^theta)^lambda$ , $xin[0,infty)$



              which can subsequently be classified as a Pareto type IV with $mu=0$ and $sigma=1$.






              share|cite|improve this answer























                up vote
                2
                down vote










                up vote
                2
                down vote









                You can show that the random variable X obeys the CDF



                $F_X(x)=1-frac1(1+x^theta)^lambda$ , $xin[0,infty)$



                which can subsequently be classified as a Pareto type IV with $mu=0$ and $sigma=1$.






                share|cite|improve this answer













                You can show that the random variable X obeys the CDF



                $F_X(x)=1-frac1(1+x^theta)^lambda$ , $xin[0,infty)$



                which can subsequently be classified as a Pareto type IV with $mu=0$ and $sigma=1$.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Aug 1 at 17:42









                DinosaurEgg

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