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Bounded Domain Distributions
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NoncentralBetaDistribution
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NoncentralBetaDistribution
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BUILT-IN MATHEMATICA SYMBOL
BetaDistribution
NoncentralFRatioDistribution
See Also »
|
Bounded Domain Distributions
New in 8.0: Alphabetical Listing
More About »
NoncentralBetaDistribution
NoncentralBetaDistribution
represents a noncentral beta distribution with shape parameters
,
and noncentrality parameter
.
MORE INFORMATION
The probability density for value
in a noncentral beta distribution is proportional to
for
, and is zero for
or
.
NoncentralBetaDistribution
allows
,
, and
to be any positive real numbers.
NoncentralBetaDistribution
can be used with such functions as
Mean
,
CDF
, and
RandomVariate
.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Probability density function:
Cumulative distribution function:
Mean and variance:
Probability density function:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
In[3]:=
Out[3]=
In[4]:=
Out[4]=
Cumulative distribution function:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
In[3]:=
Out[3]=
Mean and variance:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Scope
(6)
Generate a set of pseudorandom numbers that are beta distributed:
Compare the histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness:
Different moments with closed forms as functions of parameters:
Moment
:
Closed form for symbolic order:
CentralMoment
:
FactorialMoment
:
Cumulant
:
Hazard function:
Quantile function:
Applications
(1)
Plot the survival function of a noncentral beta distribution as a function of the noncentrality parameter:
Properties & Relations
(5)
Parameter influence on the CDF for each
:
Relationships to other distributions:
With noncentrality parameter
going to
0
, this is
BetaDistribution
:
NoncentralBetaDistribution
is a transformation of
NoncentralFRatioDistribution
:
NoncentralBetaDistribution
can be obtained as a transformation of
ChiSquareDistribution
and
NoncentralChiSquareDistribution
:
SEE ALSO
BetaDistribution
NoncentralFRatioDistribution
MORE ABOUT
Bounded Domain Distributions
New in 8.0: Alphabetical Listing
New in 8