Cumulative distribution function - Revision history

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RJJensen at 21:14, November 8, 2009

2009-11-08T21:14:47Z

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2008-12-14T16:36:24Z

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Qwestor at 19:18, January 3, 2008

2008-01-03T19:18:49Z

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2008-01-02T01:01:01Z

Qwestor at 14:15, December 31, 2007

2007-12-31T14:15:21Z

Qwestor: New page: In probability theory, a ''cumulative distribution function'' ''F(x)'' of a probability density function say ''f(x)'' is a real valued and continuous function whose value is the p...

2007-12-30T22:47:08Z

New page: In probability theory, a ''cumulative distribution function'' ''F(x)'' of a probability density function say ''f(x)'' is a real valued and continuous function whose value is the p...

New page

In [[probability theory]], a ''cumulative distribution function'' ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part real line up and including the value of that variable; i.e.,

:<math> F(x) = \int_{-\infty}^x \,f(\lambda)\,d\lambda</math>

Due to the properties of the [[probability density function]] ''f(x)'', the cumulative distribution function ''F(x)'' will have the following properties:

(1) <math> F(x) \geq 0 </math> <math> \forall x </math> inside its domain of support.

(2) <math> F(\infty) = 1 </math>, i.e., finitely convergent (to unity by convention).

(3) <math> F(a) \leq F(b) </math> for a<b, i.e., is non-decreasing

If the [[domain]] of the variable is [[finite]], then the argument in equation (2) above should be the upper bounds.

[[Category:mathematics]]

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- {|align="right" border="1"
+{|align="right" border="1"
   |+A Cumulative Distribution Function
   |-
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 If the [[domain]] of the variable is [[finite]], then the upper limit in equation (2) above should be the upper bound of the variables [[domain of support]].
-[[category:Probability and Statistics]]
+[[Category:Probability and Statistics]]

← Older revision		Revision as of 21:14, November 8, 2009
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	If the [[domain]] of the variable is [[finite]], then the upper limit in equation (2) above should be the upper bound of the variables [[domain of support]].		If the [[domain]] of the variable is [[finite]], then the upper limit in equation (2) above should be the upper bound of the variables [[domain of support]].

−	[[~~Category~~:Probability]]	+	[[category:Probability and Statistics]]

← Older revision		Revision as of 16:36, December 14, 2008
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		+	{\|align="right" border="1"
		+	\|+A Cumulative Distribution Function
		+	\|-
		+	\|[[Image:Law-uniform.png\|px=133]]
		+	\|-
		+	\|}
	In [[probability theory]], a '''cumulative distribution function''' ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,		In [[probability theory]], a '''cumulative distribution function''' ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,

@@ Line 1: / Line 1: @@
-In [[probability theory]], a ''cumulative distribution function''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,
+In [[probability theory]], a '''cumulative distribution function'''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,
@@ Line 5: / Line 5: @@
-Considering this definition in light of the fundamental theorem of the [[Integral Calculus]] yields:
+Considering this definition in light of the [[Fundamental Theorem of Calculus]] yields:
@@ Line 25: / Line 25: @@
 If the [[domain]] of the variable is [[finite]], then the upper limit in equation (2) above should be the upper bound of the variables [[domain of support]].
+[[Category:Probability]]

← Older revision		Revision as of 19:18, January 3, 2008
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	:<math> F(x) = \int_{-\infty}^x \,f(\lambda)\,d\lambda</math>		:<math> F(x) = \int_{-\infty}^x \,f(\lambda)\,d\lambda</math>
		+
		+
		+	Considering this definition in light of the fundamental theorem of the [[Integral Calculus]] yields:
		+
		+
		+	:<math> f(x) = \frac{dF(x)}{dx}</math>

← Older revision		Revision as of 01:01, January 2, 2008
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−	If the [[domain]] of the variable is [[finite]], then the upper limit equation (2) above should be the upper bound.	+	If the [[domain]] of the variable is [[finite]], then the upper limit in equation (2) above should be the upper bound of the variables [[domain of support]].


	[[Category:mathematics]]		[[Category:mathematics]]

@@ Line 1: / Line 1: @@
-In [[probability theory]], a ''cumulative distribution function''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part real line up and including the value of that variable; i.e.,
+In [[probability theory]], a ''cumulative distribution function''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,
@@ Line 11: / Line 11: @@
-(2) <math> F(\infty) = 1 </math>,  i.e., finitely convergent (to unity by convention).
+(2) <math> \lim_{x \to \infty}F(x) = 1 </math>,  i.e., finitely convergent (to unity by convention).
@@ Line 17: / Line 17: @@
-If the [[domain]] of the variable is [[finite]], then the argument in equation (2) above should be the upper bounds.
+If the [[domain]] of the variable is [[finite]], then the upper limit equation (2) above should be the upper bound.
 [[Category:mathematics]]