Expand/Contract All

Distributions Summary

Click on the distribution name to go to the look-up facility.

Name Range Parameters p.d.f c.d.f. Expectation Variance
Normal
N ( &mu. , &sigma.&powtwo. )
~y &in. &reals. &mu. &in. &reals.
&sigma.&powtwo. &in. &reals.^+
fract{1,&sqrt.${2&pi.&sigma.&powtwo.}} exp rndb{fract{- (~y - &mu.)^2,2&sigma.&powtwo. }} _ &mu. &sigma.&powtwo.
Student's t
t ( ~k )
~y &in. &reals. ~k &in. &naturals.^+ fract{&Gamma.( (~k+1)/2 ) (1 + ~y^2/~k)^{-(~k+1)/2},&Gamma.( ~k/2 ) &sqrt.${~k&pi.}} _ _ _
Chi-squared
&chi.^2 ( ~k )
~y &in. &reals.
~y > 0
~k &in. &naturals.^+ fract{~y ^{~k/2 - 1} e ^{-~y/2} , 2 ^{~k/2} &Gamma.( ~k/2 )} _ ~k 2~k
Gamma
&Gamma. (&alpha. , &beta. )
~y &in. &reals.
~y > 0
&alpha. &in. &reals.^+
&beta. &in. &reals.^+
fract{&beta.^{&alpha.} ~y^{&alpha. - 1} e^{-&beta.~y} , &Gamma.( &alpha. )} _ &alpha. ./ &beta. &alpha. ./ &beta.^2
F
F ( ~d_1 , ~d_2 )
~y &in. &reals.
~y > 0
~d_1 &in. &naturals.^+
~d_2 &in. &naturals.^+
fract{(&nu._1 ./ &nu._2) &Gamma.( (&nu._1 + &nu._2) ./ 2 ) (&nu._1 ~y ./ &nu._2)^{(&nu._1 ./ 2) - 1} , &Gamma.( &nu._1 ./ 2 ) &Gamma.( &nu._2 ./ 2 ) ( 1 + (&nu._1 ~y ./ &nu._2) )^{(&nu._1 + &nu._2) ./ 2} } _ _ _
Exponential
M( &beta. )
~y &in. &reals.
~y > 0
&beta. &in. &reals.^+

&beta. e^{- &beta.~y}

1 - e^{- &beta.~y} 1 ./ &beta. 1 ./ &beta.&powtwo.

_