Template:Loglogistic distribution characteristics: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
(Redirected page to The Loglogistic Distribution)
 
(2 intermediate revisions by one other user not shown)
Line 1: Line 1:
==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:ldaLLD10.1.gif|thumb|center|400px| ]]

Latest revision as of 09:58, 9 August 2012