Re: piecewice pdf, problems with cdf
- To: mathgroup at smc.vnet.net
- Subject: [mg105378] Re: [mg105365] piecewice pdf, problems with cdf
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 30 Nov 2009 06:11:06 -0500 (EST)
- Reply-to: hanlonr at cox.net
pdf[x_] = Piecewise[{{x^2/9, 0 < x <= 3}}];
cdf[x_] =
Assuming[{Element[x, Reals]}, Integrate[pdf[t], {t, -Infinity, x}]]
Piecewise[{{1, x > 3},
{x^3/27, Inequality[0, Less, x,
LessEqual, 3]}}]
cdf[1]
1/27
Plot[{pdf[x], cdf[x]}, {x, -1, 4},
Frame -> True, Axes -> False]
Bob Hanlon
---- michael partensky <partensky at gmail.com> wrote:
=============
Hi! Teaching the continuous distributions, I needed to introduce the
piecewise functions.
Here is the example that did not work well:
In[56]:= 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[57]:= cdf[x_] := Integrate[f1[v], {v, -\[Infinity], x}]
In[59]:= cdf[1]
Out[59]= 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?