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How to convert a univariate distribution to bivariate distribution

  1. Jun 19, 2015 #1
    hi
    i have MARSHAL-OLKIN exponential weibull distribution which have the following cdf and pdf..
    how could i convert it to bivariate distribution?
    thanks
     
  2. jcsd
  3. Jun 20, 2015 #2

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    The joint PDF of two independent random variables would just be the product of the two individual PDFs.
     
  4. Jun 20, 2015 #3
    thanks.. i have cdf and pdf (latex codes are given)..how can i make bivariate cdf from this univariate? what is shift parameter in this case? kindly guide me

    thanks alot

    \begin{align} \label{A5}
    F(x) &= \frac{1- e^{-\left(\lambda\, x+\beta\, x^k\right)}}{1-(1-\alpha)\,
    e^{-\left(\lambda\, x+\beta\, x^k\right)}}\cdot \boldsymbol I_{(0, \infty)}(x)\,,\\ \label{A6}
    f(x) &= \frac{\alpha\,\left(\lambda+ \beta \,k\,x^{k-1}\right)\, e^{-\lambda\,x-\beta\,x^k}}
    {\left(1-(1-\alpha )\, e^{-\left(\lambda\, x+\beta\, x^k\right)}\right)^2} \cdot \boldsymbol I_{(0, \infty)}(x)\,,
    \qquad \lambda, \beta, k, \alpha > 0 \,;
    \end{align}
     
  5. Jun 21, 2015 #4

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    You need to decide how you want the two variables to be related. It's easy to determine the joint PDF if they are independent -- just multiply them. Alternatively, you may want to mimic the bivariate normal, where the X and Y variables are not independent, but the vector distance from a center point (mean) is in the same class of distributions of the original distribution. For that, you may want to look at how the two coordinate vectors are related in a bivariate normal (see http://mathworld.wolfram.com/BivariateNormalDistribution.html )

    PS. My description of the bivariate normal in terms of a vector "distance" is a loose description, not to be taken literally.
     
  6. Jun 23, 2015 #5
    what is lambda, Beta, alpha, what is I(0, inf) is k the other variable with x. Is this an advanced question, whats I(0,inf)?
     
  7. Jun 24, 2015 #6
    alpha,beta ,lambda and gamma are just parameters... i have to fix three and vary one of them (the location or shift parameter)... i found that alpha is the location parameter...now i have to write these in product form with same this pdf ,beta,lambda and gamma will be fixed and alpha will vary.i dont know about (0,inf)
     
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