StudentTDistribution

StudentTDistribution[ν]
represents a Student distribution with ν degrees of freedom.

StudentTDistribution[μ,σ,ν]
represents a Student distribution with location parameter μ, scale parameter σ, and ν degrees of freedom.

DetailsDetails

  • The probability density for value in a Student distribution with degrees of freedom is proportional to . »
  • With location parameter and scale , follows a standard Student distribution with ν degrees of freedom.
  • For integer ν, the Student distribution gives the distribution of the deviation from the true mean of the observed mean for a sample of ν values from a normal distribution, normalized by standard deviation of the sample.
  • StudentTDistribution allows μ to be any real number and σ and ν to be any positive real numbers.
  • StudentTDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

ExamplesExamplesopen allclose all

Basic Examples  (8)Basic Examples  (8)

Probability density function:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Cumulative distribution function:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Mean and variance:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Median:

In[1]:=
Click for copyable input
Out[1]=

Probability density function of a generalized Student distribution:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Cumulative distribution function of a generalized Student distribution:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Mean and variance of a generalized Student distribution:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Median of a generalized Student distribution:

In[1]:=
Click for copyable input
Out[1]=
Introduced in 2007
(6.0)
| Updated in 2008
(7.0)