FPGA Central

Hello,

Who can tell me the difference between Gaussian Q-function and Error
function,who's precision is higher? for example, -3=< X<=3.

Thanks

net

[email protected] said the following on 06/09/2006 15:13:
> Who can tell me the difference between Gaussian Q-function and Error
> function,who's precision is higher? for example, -3=< X<=3.

What do you mean by "precision"? They are both well-defined functions.


--
Oli

[email protected] writes:

> Hello,
>
> Who can tell me the difference between Gaussian Q-function and Error
> function,who's precision is higher? for example, -3=< X<=3.
>
> Thanks
>
> net

http://mathworld.wolfram.com/NormalD...nFunction.html
http://mathworld.wolfram.com/Erf.html

Both functions are directly related to Gaussian functions with
zero mean. The Q function is for unit variance, while the
erf (error function) is for a variance of 1/2. The Q function
gives the value of one side, from 0 to x (for Q(x)). The
erf gives the value of both sides, from -x to +x for erf(x).

See also erfc(x) = 1 - erf(x).

Since both are defined analytically, both have infinite precision.
--
% Randy Yates % "And all that I can do
%% Fuquay-Varina, NC % is say I'm sorry,
%%% 919-577-9882 % that's the way it goes..."
%%%% <[email protected]> % Getting To The Point', *Balance of Power*, ELO
http://home.earthlink.net/~yatescr

Randy Yates wrote:

(snip)

> The Q function
> gives the value of one side, from 0 to x (for Q(x)). The
> erf gives the value of both sides, from -x to +x for erf(x).

Except that some implementations of erf() are defective and
only give results for non-negative x. I believe one in Excel
did that, either the regular one or the one in VBA, or maybe
both.

-- glen

Randy Yates wrote:

>
>The Q function
> gives the value of one side, from 0 to x (for Q(x)).

I am not sure what this statement means. The usual
definition of Q(x) is the area under the unit Gaussian
density from x to infinity. The definition applies whether
x is positive or negative. From the symmetry of the
unit Gaussian density. it follows that Q(-x) = 1 - Q(x).
Typically, the value of Q(x) for positive x is obtained
via a rational function approximation. If the standard
subroutine calculates Q(x) only for positive x, it is easy
to incorporate this calculation into a subroutine
that checks if x is negative, and then returns the
appropriate value.

--Dilip Sarwate

[email protected] writes:

> Randy Yates wrote:
>
>>
>>The Q function
>> gives the value of one side, from 0 to x (for Q(x)).
>
> I am not sure what this statement means. The usual
> definition of Q(x) is the area under the unit Gaussian
> density from x to infinity. The definition applies whether
> x is positive or negative. From the symmetry of the
> unit Gaussian density. it follows that Q(-x) = 1 - Q(x).
> Typically, the value of Q(x) for positive x is obtained
> via a rational function approximation. If the standard
> subroutine calculates Q(x) only for positive x, it is easy
> to incorporate this calculation into a subroutine
> that checks if x is negative, and then returns the
> appropriate value.

Dilip et alius,

My mistake. Yes, the Q function in communications (and the one I
should have known) is from x to infinity.

The Q(x) function (note that they don't refer to it as the "Q function")
from the Wolfram site,

http://mathworld.wolfram.com/NormalD...nFunction.html

is defined from 0 to x.

Apparently there are different definitions, but the one this
cloudy-headed dude uses in digital comm is the one from x to infinity
(see [garcia]), as you state.

--Randy

@book{garcia,
title = "Probability and Random Processes for Electrical Engineering",
author = "{Alberto~Leon-Garcia}",
publisher = "Addison-Wesley",
year = "1989"}
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <[email protected]> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr