       Re: piecewice pdf, problems with cdf

• To: mathgroup at smc.vnet.net
• Subject: [mg105379] Re: piecewice pdf, problems with cdf
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Mon, 30 Nov 2009 06:11:18 -0500 (EST)
• References: <hetheh\$fvu\$1@smc.vnet.net>

```To do calculus with piecewise functions, always use  Piecewise[]:

In:= f1[x_] := Piecewise[{  {(1/9)*x^2 , 0 < x <= 3}, {0,
True} }];
cdf[x_] := Integrate[f1[v], {v, -Infinity, x}];

Out= 1/27

--Nasser

"michael partensky" <partensky at gmail.com> wrote in message
news:hetheh\$fvu\$1 at smc.vnet.net...
> Hi! Teaching the continuous distributions, I needed to introduce the
> piecewise functions.
> Here is the example that did not work well:
>
> In:= f1[x_] /; 0 < x <= 3 := 1/9  x ^2;
> f1[x_] := 0;
>
> Plot[f1[x],{x,-1,4}] works fine. However, the results for cdf are
> ambiguous
> In:= cdf[x_] := Integrate[f1[v], {v, -\[Infinity], x}]
>
> In:= cdf
> Out= 0
>
> I thought that may be the second definition (for some reason) overwrote
> the
> first, but apparently this was not the case.
>
> Then I tried using Which,
>
> f1[x_] := Which[0 < x <= 3, x^2/9, x <= 0 || x > 3, 0];
>
> Plot[f2[x], {x, -1, 4}] worked fine.
>
> However, Plotting CDF is very slow.
>
> What is the reason for the first error and how to accelerate (compile?)
> the
> second?
>
> Thanks
> Michael
>
> PS: I was aware about the issues with the derivatives of Piecewise
> functions, but expected  integration to be safe. What did i do wrong?
>

```

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