[Rd] [Fwd: Re: pt inaccurate when x is close to 0 (PR#9945)]

[Duncan Murdoch]

Here's a contribution from Ian Smith that got bounced from the list.

-------- Original Message --------
Subject: Re: [Rd] pt inaccurate when x is close to 0 (PR#9945)
Date: Thu, 11 Oct 2007 06:02:43 -0400
From: iandjmsmith at aol.com
To: murdoch at stats.uwo.ca


Duncan,

I tried sending the rest of this to R-devel but it was rejected as spam, 
hence the personal e-mail.


R calculates the pt value from


nx = 1 + (x/n)*x;
val = pbeta(1./nx, n / 2., 0.5, /*lower_tail*/1, log_p);


whereas Gnumeric calculates the value as


val =? (n > x * x)
? pbeta (x * x / (n + x * x), 0.5, n / 2, /*lower_tail*/0, log_p)
: pbeta (n / (n + x * x), n / 2.0, 0.5, /*lower_tail*/1, log_p);


thus avoiding the loss of accuracy in the pbeta routine when 1-1./nx
is calculated.


It also makes the


if (n > 4e5) { /*-- Fixme(?): test should depend on `n' AND `x' ! */
??? /* Approx. from? Abramowitz & Stegun 26.7.8 (p.949) */
??? val = 1./(4.*n);
??? return pnorm(x*(1. - val)/sqrt(1. + x*x*2.*val), 0.0, 1.0,
???????? lower_tail, log_p);
}


code unneccessary.


Ian Smith


Personally, I think the code should also guard against the possible
overflow of the x * x expressions.


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