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Statistical Distributions - Beta Distribution - Overview and Example

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[Notation] [Density Function] [Distribution Function] [Moments Uncent.] [Expected Value] [Variance] [Mode] [Skewness] [Kurtosis] [Coeff. of Variation] [Parameter Estimation] [Random Numbers] [Properties 1] [Properties 2] [Properties 3] [Properties 4] [Properties 5] [Properties 6] [Properties 7] [Properties 8] [Properties 9] [Relationships 1] [Relationships 2] [Relationships 3] [Relationships 4] [Relationships 5] [Relationships 6] [Relationships 7] [Relationships 8] [Relationships 9] [Relationships 10] [Relationships 11] [Relationships 12] [Relationships 13] [Beta Function] [Gamma Function]

Graphical Representation of Beta Distributions - Set 1

This plot is an example of the Beta Distribution with parameters alfa=1 and beta=1. The density function is a horizontal straight line.

This plot is an example of the Beta Distribution with parameters alfa=0.75 and beta=0.75. The density function shows a U-shaped pattern.

This plot is an example of the Beta Distribution with parameters alfa=1 and beta=2. The density function is a straight line with a negative slope.

This plot is an example of the Beta Distribution with parameters alfa=2 and beta=1. The density function is a straight line with a positive slope.

Graphical Representation of Beta Distributions - Set 2

Graphical Representation of Beta Distributions - Set 3

Parameters:

Output

+-------------------+
¦ BETA DISTRIBUTION ¦
+-------------------+

MOMENTS - UNCENTERED                    STATISTICS

     1st :  3.33333333e-01              Expected Value     :       .333333
     2nd :  1.42857143e-01              Variance           :       .031746
     3rd :  7.14285714e-02              Standard Deviation :       .178174
     4th :  3.96825397e-02              Skewness           :       .467707
                                        Kurtosis           :      2.625000

MOMENTS - CENTERED                      Mode               :       .250000

     1st :  0.00000000e+00
     2nd :  3.17460317e-02
     3rd :  2.64550265e-03
     4th :  2.64550265e-03

Notation - Range - Parameters

Continuous Distributions - Beta Distribution - Notation - Range - Parameters

Density Function

Continuous Distributions - Beta Distribution - Density Function

Distribution Function

Continuous Distributions - Beta Distribution - Distribution Function

Uncentered Moments

Continuous Distributions - Beta Distribution - Moments Uncent.

Expected Value

Continuous Distributions - Beta Distribution - Expected Value

Variance

Continuous Distributions - Beta Distribution - Variance

Mode

Continuous Distributions - Beta Distribution - Mode

Skewness

Continuous Distributions - Beta Distribution - Skewness

Kurtosis

Continuous Distributions - Beta Distribution - Kurtosis

Coefficient of Variation

Continuous Distributions - Beta Distribution - Coefficient of Variation

Parameter Estimation

Continuous Distributions - Beta Distribution - Parameter Estimation

Random Number Generator

Continuous Distributions - Beta Distribution - Random Number Generator

Distribution Function

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