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I want to calculate Cumulative distribution function of Y, when Y is a Random Variable (Y=min{X,X'}) and X is a piecewise defined function Random variable. CDF of X is something like this code: 

if (0<x<A) then FX = B(x)
 else if (A<x<A^2) then FX = D(x)

I know that FY=1-((1-FX)^2). But it doesn't work when X is a piecewise defined function. How can I calculate FY?

user5254345
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    What is a "multidisciplinary function"? Do you mean "multivariable function"? What is `X`? `A`? `B`? `D`? `F`? You really need to explain what you mean rather than dropping symbols and hoping that we can guess your meaning. In any event, this is off-topic in Stack Overflow since it is more about mathematics then computing. – John Coleman Nov 16 '16 at 11:01
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    Perhaps by "multidisciplinary" you mean "piecewise defined"? If so, how can two pieces have the same defining condition (`(0 – John Coleman Nov 16 '16 at 11:47
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    Thank U for ur response. 1. Yes exactly I mean that X is a piecewise defined function and consequently Y will be too. 2. range of x was a mistake. I edited that. 3. I compared CDF of simulated data on matlab with Function that I calculated by G(y) = 1 - (1 - F(x)))^2, and they weren't same. They had small differences in the middle of plot. – user5254345 Nov 16 '16 at 13:22
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    Round-off error? Sampling error if you are doing a simulation? Perhaps there is a bug in your simulation or in your formula for `F`. Mathematically, the fact that `F` is piecewise-defined isn't relevant. – John Coleman Nov 16 '16 at 14:55
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    Without knowing what the functions are and how the simulation was done, it is impossible to know whether or not there is anything surprising about the image that you posted. A curve generated by Monte Carlo methods almost never matches a theoretical curve. – John Coleman Nov 16 '16 at 17:24
  • Thank you for your response. and you mean I should explain all functions here? I'm sure simulation is correct. I 'm going to check functions again :( – user5254345 Nov 16 '16 at 17:30
  • Explaining what the cdf of `X` is wouldn't hurt. If it is piecewise defined, then the cdf of `Y` would similarly be piecewise defined, though I don't see how `1-((1-B(x))(1-D(x)))` could be one of the pieces. – John Coleman Nov 16 '16 at 17:38

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