Template:Characteristics of the gamma distribution - Revision history

Lisa Hacker: Redirected page to The Gamma Distribution

2012-08-08T07:43:09Z

Redirected page to The Gamma Distribution

← Older revision		Revision as of 07:43, 8 August 2012
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	~~===Characteristics of the Gamma Distribution===~~		#REDIRECT [[The_Gamma_Distribution]]

	~~Some of the specific characteristics of the gamma distribution are the following:~~

	~~For <math>k>1</math> :~~
	~~:• As <math>t\to 0,\infty </math> , <math>f(t)\to 0.</math>~~
	~~:• <math>f(t)</math> increases from 0 to the mode value and decreases thereafter.~~
	~~:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>~~
	~~:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>~~
	~~:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.~~
	~~:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>~~

	[[~~Image:BSpdf1.png\|center\|250px\| ]]~~

	~~For <math>k=1</math> :~~
	~~:• Gamma becomes the exponential distribution.~~
	~~:• As <math>t\to 0</math> , <math>f(T)\to \tfrac{1}{{{e}^{\mu }}}.</math>~~
	~~:• As <math>t\to \infty ,f(t)\to 0.</math>~~
	~~:• The <math>pdf</math> decreases monotonically and is convex.~~
	~~:• <math>\lambda (t)\equiv \tfrac{1}{{{e}^{\mu }}}</math> . <math>\lambda (t)</math> is constant.~~
	~~:• The mode does not exist.~~

	~~[[Image:BSpdf2.png\|center\|250px\| ]]~~

	~~For <math>0<k<1</math> :~~
	~~:• As <math>t\to 0</math> , <math>f(t)\to \infty .</math>~~
	~~:• As <math>t\to \infty ,f(t)\to 0.</math>~~
	~~:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>~~
	~~:• The <math>pdf</math> decreases monotonically and is convex.~~
	~~:• As <math>\mu </math> increases, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.~~
	~~:• As <math>\mu </math> decreases, the <math>pdf</math> shifts towards the left and its height increases.~~
	~~:• The mode does not exist.~~

	~~[[Image:BSpdf3.png\|center\|250px\|~~ ]]

Nicolette Young: /* Characteristics of the Gamma Distribution */

2012-04-25T21:57:12Z

Characteristics of the Gamma Distribution

← Older revision		Revision as of 21:57, 25 April 2012
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	:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>		:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>

	[[Image:BSpdf1.png\|center\|~~400px~~\| ]]		[[Image:BSpdf1.png\|center\|250px\| ]]

	For <math>k=1</math> :		For <math>k=1</math> :
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	:• The mode does not exist.		:• The mode does not exist.

	[[Image:BSpdf2.png\|center\|~~400px~~\| ]]		[[Image:BSpdf2.png\|center\|250px\| ]]

	For <math>0<k<1</math> :		For <math>0<k<1</math> :
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	:• The mode does not exist.		:• The mode does not exist.

	[[Image:BSpdf3.png\|center\|~~400px~~\| ]]		[[Image:BSpdf3.png\|center\|250px\| ]]

Nicolette Young: /* Characteristics of the Gamma Distribution */

2012-03-14T19:00:43Z

Characteristics of the Gamma Distribution

← Older revision		Revision as of 19:00, 14 March 2012
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	:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>		:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>

	[[Image:~~ldaGD10~~.~~1.gif\|thumb~~\|center\|400px\| ]]		[[Image:BSpdf1.png\|center\|400px\| ]]

	For <math>k=1</math> :		For <math>k=1</math> :
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	:• The mode does not exist.		:• The mode does not exist.

	[[Image:~~ldaGD10~~.~~2.gif\|thumb~~\|center\|400px\| ]]		[[Image:BSpdf2.png\|center\|400px\| ]]

	For <math>0<k<1</math> :		For <math>0<k<1</math> :
Line 32:		Line 32:
	:• The mode does not exist.		:• The mode does not exist.

	[[Image:~~ldaGD10~~.~~3.gif\|thumb~~\|center\|400px\| ]]		[[Image:BSpdf3.png\|center\|400px\| ]]

Harry Guo: /* Characteristics of the Gamma Distribution */

2012-02-14T22:24:07Z

Characteristics of the Gamma Distribution

← Older revision		Revision as of 22:24, 14 February 2012
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	For <math>k=1</math> :		For <math>k=1</math> :
	:• Gamma becomes the exponential distribution.		:• Gamma becomes the exponential distribution.
	:• As <math>T\to 0</math> , <math>f(T)\to \tfrac{1}{{{e}^{\mu }}}.</math>		:• As <math>t\to 0</math> , <math>f(T)\to \tfrac{1}{{{e}^{\mu }}}.</math>
	:• As <math>T\to \infty ,f(T)\to 0.</math>		:• As <math>t\to \infty ,f(t)\to 0.</math>
	:• The <math>pdf</math> decreases monotonically and is convex.		:• The <math>pdf</math> decreases monotonically and is convex.
	:• <math>\lambda (T)\equiv \tfrac{1}{{{e}^{\mu }}}</math> . <math>\lambda (T)</math> is constant.		:• <math>\lambda (t)\equiv \tfrac{1}{{{e}^{\mu }}}</math> . <math>\lambda (t)</math> is constant.
	:• The mode does not exist.		:• The mode does not exist.

Harry Guo: /* Characteristics of the Gamma Distribution */

2012-02-14T22:23:25Z

Characteristics of the Gamma Distribution

← Older revision		Revision as of 22:23, 14 February 2012
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	:• <math>f(t)</math> increases from 0 to the mode value and decreases thereafter.		:• <math>f(t)</math> increases from 0 to the mode value and decreases thereafter.
	:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>		:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>
	:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>		:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>
	:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.		:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.
			:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>
	As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>

	[[Image:ldaGD10.1.gif\|thumb\|center\|400px\| ]]		[[Image:ldaGD10.1.gif\|thumb\|center\|400px\| ]]

Harry Guo: /* Characteristics of the Gamma Distribution */

2012-02-14T22:22:16Z

Characteristics of the Gamma Distribution

← Older revision		Revision as of 22:22, 14 February 2012
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	===Characteristics of the Gamma Distribution===		===Characteristics of the Gamma Distribution===

	Some of the specific characteristics of the gamma distribution are the following:		Some of the specific characteristics of the gamma distribution are the following:

	For <math>k>1</math> :		For <math>k>1</math> :
	:• As <math>T\to 0,\infty </math> , <math>f(T)\to 0.</math>		:• As <math>t\to 0,\infty </math> , <math>f(t)\to 0.</math>
	:• <math>f(T)</math> increases from 0 to the mode value and decreases thereafter.		:• <math>f(t)</math> increases from 0 to the mode value and decreases thereafter.
	:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>		:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>t={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>
	:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>		:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>
	:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.		:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.

	As <math>T\to \infty ,\lambda (T)\to \tfrac{1}{{{e}^{\mu }}}.</math>		As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>

	[[Image:ldaGD10.1.gif\|thumb\|center\|400px\| ]]		[[Image:ldaGD10.1.gif\|thumb\|center\|400px\| ]]
Line 24:		Line 25:

	For <math>0<k<1</math> :		For <math>0<k<1</math> :
	:• As <math>T\to 0</math> , <math>f(T)\to \infty .</math>		:• As <math>t\to 0</math> , <math>f(t)\to \infty .</math>
	:• As <math>T\to \infty ,f(T)\to 0.</math>		:• As <math>t\to \infty ,f(t)\to 0.</math>
	:• As <math>T\to \infty ,\lambda (T)\to \tfrac{1}{{{e}^{\mu }}}.</math>		:• As <math>t\to \infty ,\lambda (t)\to \tfrac{1}{{{e}^{\mu }}}.</math>
	:• The <math>pdf</math> decreases monotonically and is convex.		:• The <math>pdf</math> decreases monotonically and is convex.
	:• As <math>\mu </math> increases, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.		:• As <math>\mu </math> increases, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.

Nicolette Young: Created page with '===Characteristics of the Gamma Distribution=== Some of the specific characteristics of the gamma distribution are the following: For $k>1$ : :• As $T\to 0,\…'$

2012-01-04T21:24:44Z

Created page with '===Characteristics of the Gamma Distribution=== Some of the specific characteristics of the gamma distribution are the following: For <math>k>1</math> : :• As <math>T\to 0,\…'

New page

===Characteristics of the Gamma Distribution===
Some of the specific characteristics of the gamma distribution are the following:

For <math>k>1</math> :
:• As <math>T\to 0,\infty </math> , <math>f(T)\to 0.</math>
:• <math>f(T)</math> increases from 0 to the mode value and decreases thereafter.
:• If <math>k\le 2</math> then <math>pdf</math> has one inflection point at <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}+1).</math>
:• If <math>k>2</math> then <math>pdf</math> has two inflection points for <math>T={{e}^{\mu }}\sqrt{k-1}(</math> <math>\sqrt{k-1}\pm 1).</math>
:• For a fixed <math>k</math> , as <math>\mu </math> increases, the <math>pdf</math> starts to look more like a straight angle.

As <math>T\to \infty ,\lambda (T)\to \tfrac{1}{{{e}^{\mu }}}.</math>

[[Image:ldaGD10.1.gif|thumb|center|400px| ]]

For <math>k=1</math> :
:• Gamma becomes the exponential distribution.
:• As <math>T\to 0</math> , <math>f(T)\to \tfrac{1}{{{e}^{\mu }}}.</math>
:• As <math>T\to \infty ,f(T)\to 0.</math>
:• The <math>pdf</math> decreases monotonically and is convex.
:• <math>\lambda (T)\equiv \tfrac{1}{{{e}^{\mu }}}</math> . <math>\lambda (T)</math> is constant.
:• The mode does not exist.

[[Image:ldaGD10.2.gif|thumb|center|400px| ]]

For <math>0<k<1</math> :
:• As <math>T\to 0</math> , <math>f(T)\to \infty .</math>
:• As <math>T\to \infty ,f(T)\to 0.</math>
:• As <math>T\to \infty ,\lambda (T)\to \tfrac{1}{{{e}^{\mu }}}.</math>
:• The <math>pdf</math> decreases monotonically and is convex.
:• As <math>\mu </math> increases, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.
:• As <math>\mu </math> decreases, the <math>pdf</math> shifts towards the left and its height increases.
:• The mode does not exist.

[[Image:ldaGD10.3.gif|thumb|center|400px| ]]

Template:Characteristics of the gamma distribution - Revision history

Lisa Hacker: Redirected page to The Gamma Distribution

Nicolette Young: /* Characteristics of the Gamma Distribution */

Nicolette Young: /* Characteristics of the Gamma Distribution */

Harry Guo: /* Characteristics of the Gamma Distribution */

Harry Guo: /* Characteristics of the Gamma Distribution */

Harry Guo: /* Characteristics of the Gamma Distribution */

Nicolette Young: Created page with '===Characteristics of the Gamma Distribution=== Some of the specific characteristics of the gamma distribution are the following: For k>1 : :• As T\to 0,\…'

Nicolette Young: Created page with '===Characteristics of the Gamma Distribution=== Some of the specific characteristics of the gamma distribution are the following: For $k>1$ : :• As $T\to 0,\…'$