Template:Loglogistic distribution characteristics: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
(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…')
 
(Redirected page to The Loglogistic Distribution)
 
(4 intermediate revisions by 2 users 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