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which polynomial interpolant is good for CDFrepresentation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67944] which polynomial interpolant is good for CDFrepresentation
  • From: glare22 at gmail.com
  • Date: Thu, 13 Jul 2006 06:54:27 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I want to get the value of random variables corresponding to a set of
CDF( cumulative density function) points( or collocation points). I
have thought to use a set of uniform distributed variables to get the
cdf and then use a polynomial interpolant to fit the cdf curve and use
interplolant to get the random variables from a set of cdf points.
e.g.
y_i=cdf(x_i), (x_i, are selected from small value to a large value in
uniform interval)
xo_i=polyf(y_i,x_i,yo_i), (yo_i are the collocation points of cdf, xo_i
are what I want from the corresponding collocation points. polyf()
denotes the polynomial interpolant function)

But many problems happen, sometimes the results oscillate.Sometimes it
cannot get any results, since some values of cdf are indistinctive,
like upper to some level, all the cdf equal to 1.0. How can I  do? Does
the problem exist in the method? Or a proper choice of polynomial
interpolant will help this problem. Is there a good way to represent
the cdf by choosing a set of proper ramdom variables to avoid the
undistinct of the cdf value? Thanks a lot.



Liang


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