Template:Loglogistic distribution characteristics - Revision history

Lisa Hacker: Redirected page to The Loglogistic Distribution

2012-08-09T09:58:49Z

Redirected page to The Loglogistic Distribution

← Older revision		Revision as of 09:58, 9 August 2012
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	~~==Distribution Characteristics==~~		#REDIRECT [[The_Loglogistic_Distribution]]
	~~For <math>\sigma >1</math> :~~

	~~:* <math>f(t)</math> decreases monotonically and is convex. Mode and mean do not exist.~~

	~~For <math>\sigma =1</math> :~~

	~~:* <math>f(t)</math> decreases monotonically and is convex. Mode and mean do not exist. As <math>t\to 0</math> , <math>f(t)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>~~
	~~:* As <math>t\to 0</math> , <math>\lambda (t)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>~~

	~~For <math>0<\sigma <1</math> :~~

	~~:* The shape of the loglogistic distribution is very similar to that of the lognormal distribution and the Weibull distribution.~~
	~~:* The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.~~
	~~:* As <math>\mu </math> increases, while <math>\sigma </math> is kept the same, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.~~
	~~:* As <math>\mu </math> decreases,while <math>\sigma </math> is kept the same, the .. gets pushed in towards the left and its height increases.~~
	:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.

	[[~~Image:WB.15 loglogistic pdf.png\|center\|250px\|~~ ]]

Nicolette Young: /* Distribution Characteristics */

2012-04-25T21:59:04Z

Distribution Characteristics

← Older revision		Revision as of 21:59, 25 April 2012
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	:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.		:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.

	[[Image:WB.15 loglogistic pdf.png\|center\|~~400px~~\| ]]		[[Image:WB.15 loglogistic pdf.png\|center\|250px\| ]]

Nicolette Young: /* Distribution Characteristics */

2012-03-15T17:24:07Z

Distribution Characteristics

← Older revision		Revision as of 17:24, 15 March 2012
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	:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.		:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.

	[[Image:~~ldaLLD10~~.1.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.15 loglogistic pdf.png\|center\|400px\| ]]

Harry Guo at 17:47, 20 February 2012

2012-02-20T17:47:40Z

← Older revision		Revision as of 17:47, 20 February 2012
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	====Distribution Characteristics====		==Distribution Characteristics==
	For <math>\sigma >1</math> :		For <math>\sigma >1</math> :

Harry Guo: /* Distribution Characteristics */

2012-02-15T01:52:21Z

Distribution Characteristics

← Older revision		Revision as of 01:52, 15 February 2012
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	For <math>\sigma >1</math> :		For <math>\sigma >1</math> :

	:• <math>f(T)</math> decreases monotonically and is convex. Mode and mean do not exist.		:* <math>f(t)</math> decreases monotonically and is convex. Mode and mean do not exist.

	For <math>\sigma =1</math> :		For <math>\sigma =1</math> :

	:• <math>f(T)</math> decreases monotonically and is convex. Mode and mean do not exist. As <math>T\to 0</math> , <math>f(T)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>		:* <math>f(t)</math> decreases monotonically and is convex. Mode and mean do not exist. As <math>t\to 0</math> , <math>f(t)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>
	:• As <math>T\to 0</math> , <math>\lambda (T)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>		:* As <math>t\to 0</math> , <math>\lambda (t)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>

	For <math>0<\sigma <1</math> :		For <math>0<\sigma <1</math> :

	:• The shape of the loglogistic distribution is very similar to that of the lognormal distribution and the Weibull distribution.		:* The shape of the loglogistic distribution is very similar to that of the lognormal distribution and the Weibull distribution.
	:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.		:* The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.
	:• As <math>\mu </math> increases, while <math>\sigma </math> is kept the same, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.		:* As <math>\mu </math> increases, while <math>\sigma </math> is kept the same, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.
	:• As <math>\mu </math> decreases,while <math>\sigma </math> is kept the same, the .. gets pushed in towards the left and its height increases.		:* As <math>\mu </math> decreases,while <math>\sigma </math> is kept the same, the .. gets pushed in towards the left and its height increases.
	:• <math>\lambda (T)</math> increases till <math>T={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (T)</math> is concave at first, then becomes convex.		:* <math>\lambda (t)</math> increases till <math>t={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (t)</math> is concave at first, then becomes convex.

	[[Image:ldaLLD10.1.gif\|thumb\|center\|400px\| ]]		[[Image:ldaLLD10.1.gif\|thumb\|center\|400px\| ]]

Nicolette Young: Created page with '====Distribution Characteristics==== For $\sigma >1$ : :• $f(T)$ decreases monotonically and is convex. Mode and mean do not exist. For $\sigma…'$

2012-01-04T22:32:29Z

Created page with '====Distribution Characteristics==== For <math>\sigma >1</math> : :• <math>f(T)</math> decreases monotonically and is convex. Mode and mean do not exist. For <math>\sigma…'

New page

====Distribution Characteristics====
For <math>\sigma >1</math> :

:• <math>f(T)</math> decreases monotonically and is convex. Mode and mean do not exist.

For <math>\sigma =1</math> :

:• <math>f(T)</math> decreases monotonically and is convex. Mode and mean do not exist. As <math>T\to 0</math> , <math>f(T)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>
:• As <math>T\to 0</math> , <math>\lambda (T)\to \tfrac{1}{\sigma {{e}^{\tfrac{\mu }{\sigma }}}}.</math>

For <math>0<\sigma <1</math> :

:• The shape of the loglogistic distribution is very similar to that of the lognormal distribution and the Weibull distribution.
:• The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.
:• As <math>\mu </math> increases, while <math>\sigma </math> is kept the same, the <math>pdf</math> gets stretched out to the right and its height decreases, while maintaining its shape.
:• As <math>\mu </math> decreases,while <math>\sigma </math> is kept the same, the .. gets pushed in towards the left and its height increases.
:• <math>\lambda (T)</math> increases till <math>T={{e}^{\mu +\sigma \ln (\tfrac{1-\sigma }{\sigma })}}</math> and decreases thereafter. <math>\lambda (T)</math> is concave at first, then becomes convex.

[[Image:ldaLLD10.1.gif|thumb|center|400px| ]]

Template:Loglogistic distribution characteristics - Revision history

Lisa Hacker: Redirected page to The Loglogistic Distribution

Nicolette Young: /* Distribution Characteristics */

Nicolette Young: /* Distribution Characteristics */

Harry Guo at 17:47, 20 February 2012

Harry Guo: /* Distribution Characteristics */

Nicolette Young: Created page with '====Distribution Characteristics==== For \sigma >1 : :• f(T) decreases monotonically and is convex. Mode and mean do not exist. For \sigma…'

Nicolette Young: Created page with '====Distribution Characteristics==== For $\sigma >1$ : :• $f(T)$ decreases monotonically and is convex. Mode and mean do not exist. For $\sigma…'$