# Gaussian normal distribution curve

1. Nov 9, 2004

### touqra

I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, $$f(x \geq X) = 0$$, but, $$f(x \leq X) =$$a function which has a Gaussian shape-like curve.
Is there one such as this that you know or in mathematics literatures?

2. Nov 9, 2004

### TenaliRaman

define the Gaussian for any finite interval
f(x)
= gaussian for a<x<b
= 0 otherwise

-- AI

3. Nov 9, 2004

### Galileo

Or consider:
$$f(x)=Ae^{-x^2}-b$$
for $|x|<\sqrt{\ln(A/b)}$ and 0 elswhere.
That one is even continuous.

4. Nov 9, 2004

### uart

Or even just a raised cosine, 1 + cos(x) : -pi < x < pi .

5. Nov 9, 2004

### touqra

Is there a mathematical function which is not piece-wise and can be defined for the whole range of x (just by one mathematical relationship)?

6. Nov 9, 2004

### matt grime

Probably not since you are splitting the range up in your own requirements, besides, that is purely a superficial issue for you. If you know what a heaviside function is then, for k some positive real number

H(x+k)(1-H(x-k))f(x)

for some suitably shaped and nomalized function would do and would appear to be a nice single line wouldn't it? Of course

H(y) is defined piecewise.