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Likelihood Function

Usage

Likelihood[dist, {x1, x2, ...}] gives the likelihood function for observations x1, x2, ... from the distribution dist.
Likelihood[proc, {{t1, x1}, {t2, x2}, ...}] gives the likelihood function for the observations xi at time ti from the process proc.
Likelihood[proc, {path1, path2, ...}] gives the likelihood function for observations from path1, path2, ... from the process proc.

Basic examples

$Get the likelihood function for a normal distribution: In[1]:=Likelihood[NormalDistribution[μ, σ], {x_1, x_2, x_3, x_4, x_5}] Out[1]=e^(-((-μ + x_1)^2 + (-μ + x_2)^2 + (-μ + x_3)^2 + (-μ + x_4)^2 + (-μ + x_5)^2)/(2 σ^2))/(4 sqrt(2) π^(5/2) σ^5) Compute a likelihood for numeric data: In[1]:=data=RandomVariate[GammaDistribution[2, 3], 100]; In[2]:=Likelihood[GammaDistribution[2, 3], data] Out[2]=1.279×10^-115 Plot likelihood contours as a function of α and β on a log scale: In[3]:=ContourPlot[Log[Likelihood[GammaDistribution[α, β], data]], {α, 1, 3}, {β, 1, 5}] Out[3]= Compute the likelihood for multivariate data: In[1]:=data=RandomVariate[BinormalDistribution[.8], 100]; In[2]:=Likelihood[BinormalDistribution[ρ], data] Out[2]=e^(-(210.687 - 173.083 ρ)/(2 (1 - ρ^2)))/(1267650600228229401496703205376 π^100 (1 - ρ^2)^50)$

Attributes

Protected | ReadProtected

Relationships with other entities

LogLikelihood | PDF | EstimatedDistribution

Relationships with other entities

Typical ranks of usage in programs

2685th most common (1 in 1210000 symbols)

1431st most common (1 in 30100 symbols)

History

introduced in Version 8 (November 2010)
last modified in Version 10 (July 2014)

Timeline

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