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[Bug-gsl] CDF documentation bug
From: |
Jussi Piitulainen |
Subject: |
[Bug-gsl] CDF documentation bug |
Date: |
28 Jan 2004 18:41:46 +0200 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.2 |
Dear bug,
I think a formula in an info node for gsl-1.4 is not quite right. The
text of the node is cut and pasted below, with the formula for "CDF
for the upper tail" marked with asterisks.
It says P(x) = \int_{x}^{-\infty}
but should say Q(x) = \int_{x}^{+\infty}, I think.
(Also, the word "value" is missing in the description of Q. It says
"taking a greater than x".)
The info node follows.
File: gsl-ref.info, Node: Random Number Distribution Introduction,
Next: The Gaussian Distribution, Up: Random Number Distributions
Introduction
============
Continuous random number distributions are defined by a probability
density function, p(x), such that the probability of x occurring in the
infinitesimal range x to x+dx is p dx.
The cumulative distribution function for the lower tail is defined
by,
P(x) = \int_{-\infty}^{x} dx' p(x')
and gives the probability of a variate taking a value less than x.
The cumulative distribution function for the upper tail is defined
by,
**** P(x) = \int_{x}^{-\infty} dx' p(x') ****
and gives the probability of a variate taking a greater than x. The
upper and lower cumulative distribution functions are related by P(x) +
Q(x) = 1 and satisfy 0 <= P(x) <= 1, 0 <= Q(x) <= 1.
The inverse cumulative distributions, x=P^{-1}(P) and x=Q^{-1}(Q)
give the values of x which correspond to a specific value of P or Q.
They can be used to find confidence limits from probability values.
- [Bug-gsl] CDF documentation bug,
Jussi Piitulainen <=