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Statistical Distributions - Beta Distribution - Overview and Example

[Home] [Up] [Overview] [Inverted Beta] [Cauchy 1] [Cauchy 2 Param.] [Chi] [Chi Sq. 1 Param.] [Chi Sq. 2 Param.] [Erlang] [Exponential] [Fisher F] [Gamma] [Inverted Gamma] [Gumbel] [Laplace] [Logistic] [Lognormal] [Normal] [Pareto] [Power] [Rayleigh] [r-Distribution] [Rect. (Uniform)] [Student t] [Triangular] [Weibull] [Beta]

[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.

alfa=1 beta=1

alfa=0.75 beta=0.75

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.

alfa=1 beta=2

alfa=2 beta=1

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

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Home
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Overview
Inverted Beta
Cauchy 1
Cauchy 2 Param.
Chi
Chi Sq. 1 Param.
Chi Sq. 2 Param.
Erlang
Exponential
Fisher F
Gamma
Inverted Gamma
Gumbel
Laplace
Logistic
Lognormal
Normal
Pareto
Power
Rayleigh
r-Distribution
Rect. (Uniform)
Student t
Triangular
Weibull
Beta
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
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