Science Fair Project Encyclopedia

Science Fair Project Encyclopedia Contents Page

Identifiability condition

In mathematics, the identifiability condition is defined as

$f(x) = f(y) \Leftrightarrow x = y \quad \forall x,y$

which says that if a function evaluates the same then the arguments must be the same. I.e., a function is "identifiable" iff it is one-to-one. The article on injective functions deals with this same topic more abstractly.

Example 1

Let the function be the sine function. This function does not satisfy the condition when the parameter is allowed to take any real number.

$\sin(0) = 0 = \sin(2\pi) = \sin(2\pi) = \cdots$

However, if the parameter is restricted to $[0,2π)$ then it satisifies the condition

Example 2

Let the function be $y = f (x) = x 3$ . This function clearly satisfies the condition as it is a one-to-one function.

Example 3

Let the function be the normal distribution with zero mean. For a fixed random value and nonfixed variance this function satisfies the condition

$f(x; \sigma_1^2) = f(x; \sigma_2^2) \Leftrightarrow \sigma_1^2 = \sigma_2^2$

Categories: Elementary mathematics

Last updated: 05-28-2005 22:42:15

Science Fair Project Encyclopedia Contents Page

10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details

All Science Fair Projects