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Hi All,

My college book, Probability & Stochastic Processes For Engineers,
Carl Helstrom, 2nd Edition:

http://www.amazon.com/Probability-St.../dp/0023535717

says that erfc(0) is 0.5.

Wikipedia says that it is 1.0 [see table at bottom of article]:

http://en.wikipedia.org/wiki/Error_function

-Le Chaud Lapin-

On Apr 18, 12:52*pm, Le Chaud Lapin <jaibudu...@gmail.com> wrote:
> Hi All,
>
> My college book, Probability & Stochastic Processes For Engineers,
> Carl Helstrom, 2nd Edition:
>
> http://www.amazon.com/Probability-St...Engineers-Hels...
>
> says that erfc(0) is 0.5.
>
> Wikipedia says that it is 1.0 [see table at bottom of article]:
>
> http://en.wikipedia.org/wiki/Error_function
>

it's all in the definition. most say that erf(0) is 0 and

erfc(x) + erf(x) = 1

your college book is scaling and offsetting them both so that it is
directly the probability distribution function for the normal random
variable. it seems logical to me, but sometimes we need to submit to
illogical, but widely-used convention.

r b-j

On Apr 18, 1:11*pm, robert bristow-johnson <r...@audioimagination.com>
wrote:
> On Apr 18, 12:52*pm, Le Chaud Lapin <jaibudu...@gmail.com> wrote:
>
> > Hi All,
>
> > My college book, Probability & Stochastic Processes For Engineers,
> > Carl Helstrom, 2nd Edition:
>
> >http://www.amazon.com/Probability-St...Engineers-Hels...
>
> > says that erfc(0) is 0.5.
>
> > Wikipedia says that it is 1.0 [see table at bottom of article]:
>
> >http://en.wikipedia.org/wiki/Error_function
>
> it's all in the definition. *most say that erf(0) is 0 and
>
> * erfc(x) + erf(x) = 1
>
> your college book is scaling and offsetting them both so that it is
> directly the probability distribution function for the normal random
> variable. *it seems logical to me, but sometimes we need to submit to
> illogical, but widely-used convention.

My book (Helstrom) also calls the complementary error function, erfc
(x), the "error function". He does this throughout the book, which is
very confusing on first sight.

I also recall in a materials science course in college that a
professor did the same thing, which was even more confusing back then.

I think that the person who originally devised the terms "error
function" and "complementary error function" probably knew what he was
doing. I would also venture to say that the "c" at the end of erfc
means "complementary", in which case, savants in this field should not
be calling the complementary error function, "error function."

B. L. Whorf would roll in his grave.

-Le Chaud Lapin-

Le Chaud Lapin <[email protected]> wrote:
(snip)

> I also recall in a materials science course in college that a
> professor did the same thing, which was even more confusing back then.

Maybe not so much different than calling cos() a sine function,
which it is if you shift it over a little bit.

-- glen

glen herrmannsfeldt wrote:
> Le Chaud Lapin <[email protected]> wrote:
> (snip)
>
>> I also recall in a materials science course in college that a
>> professor did the same thing, which was even more confusing
>> back then.
>
> Maybe not so much different than calling cos() a sine function,
> which it is if you shift it over a little bit.

Who does that? SinusOID, yes -- and that's all I've seen so far.


Martin

--
Quidquid latine scriptum est, altum videtur.

On May 7, 4:17*am, Martin Eisenberg <martin.eisenb...@udo.edu> wrote:
> glen herrmannsfeldt wrote:
> > Le Chaud Lapin <jaibudu...@gmail.com> wrote:
> > (snip)
>
> >> I also recall in a materials science course in college that a
> >> professor did the same thing, which was even more confusing
> >> back then.
>
> > Maybe not so much different than calling cos() a sine function,
> > which it is if you shift it over a little bit. *
>
> Who does that? SinusOID, yes -- and that's all I've seen so far.

Also, I think there is something wrong with calling cos() 'the' sine
function instead of 'a' sign function.

Of course, Glen, I see nothing wrong with saying that a function is in
same family of functions, that one could be used in place of any in
family with proper adjustment.

However, Helstrom is not using erfc(x) in that sense. He is saying
that it is the error function, as opposed to the complementary error
function.

Also, looking further last night, I saw that some authors cast away or
alter the constant on outside of integrals for erfc(x), and erf(x).
Doing this might rob reader of potential insight into subtle,
underlying semantics [Fourier integral constant comes to mind here,
too.]

Seems to me that an intuitive example might be to drop a ball bearing
from top center of grain silo that has doors open at bottom,
distributed symmetrically around the perimenter, into which random
wind with zero mean blows. The governing PDF, as function of distance
r from center line, at least up to the radius of silo, would be
Guassian with zero mean and variance determined by individual
variances of PDF's of wind functions. One could then regard the
probability that the bearing hits the wall of the silo before hitting
the ground as the error function. This would be different from many
other definitions of error functions, but might make sense intuitively
for this particular situation.

Perhaps the physical model should be described for each definition of
erfc, erf.

-Le Chaud Lapin-