Re: Creating/Solving a cumulative distribution function?
- To: mathgroup at smc.vnet.net
- Subject: [mg41787] Re: [mg41768] Creating/Solving a cumulative distribution function?
- From: Bobby Treat <drmajorbob-MathGroup3528 at mailblocks.com>
- Date: Thu, 5 Jun 2003 07:31:30 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
g[x_] := (2/Pi)*(1 - Cos[4x ])
gcdf[x_] = Integrate[g[x], {x, 0, x}]
Plot[gcdf[x], {x, 0, Pi/2}]
r = Random[Real, {0, 1}]
FindRoot[gcdf[x] == r, {x, Pi/4}]
Cos and Sin expect arguments in Radians, and this becomes a completely
different problem if you pose it in degrees:
g[x_] := (2/Pi)*(1 - Cos[4x (180/Pi)])
gcdf[x_] = Integrate[g[x], {x, 0, x}]
Plot[gcdf[x], {x, 0, 90}]
r = Random[Real, {0, 1}]
FindRoot[gcdf[x] == r, {x, 45}]
Bobby
-----Original Message-----
From: Jonathan Greenberg <greenberg at ucdavis.edu>
To: mathgroup at smc.vnet.net
Subject: [mg41787] [mg41768] Creating/Solving a cumulative distribution function?
Hi there, I was hoping one of you could help me out with a CDF problem
I'm having. I have a PDF: g[x_]:=(2/Pi)*(1-Cos[4x]) where x ranges from
0 Degree to 90 Degree I understand the basic idea of a CDF, that I can
integrate from 0 to some arbitary value (y) between (0,90) to get the
cumulative probability:
gcdf[x_]:=Evaluate[Integrate[g[x],{x,0Degree,x}] I'd like to Solve for
x, given: gcdf[x]==Random[Real,0,1] where 0Degree>=x>=90Degree
Solve, NSolve and FindRoot don't appear to be working correctly -- can
someone give me a hand solving this equation? --j