How to convert a univariate distribution to bivariate distribution

1. Jun 19, 2015

samrah

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. Jun 20, 2015

FactChecker

The joint PDF of two independent random variables would just be the product of the two individual PDFs.

3. Jun 20, 2015

samrah

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}

4. Jun 21, 2015

FactChecker

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.

5. Jun 23, 2015

Josh S Thompson

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)?

6. Jun 24, 2015

samrah

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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