Beta Type II Distribution Calculator

Beta Type II Distribution Calculator

Beta Type II Distribution Calculator is used to find the probability density and cumulative probabilities for Beta Type II distribution with parameter $\alpha$ and $\beta$.

Beta Type II Distribution Calculator
First Parameter $\alpha$:
Second Parameter $\beta$
Value of x
Results
Probability density : f(x)
Probability X less than x: P(X < x)
Probability X greater than x: P(X > x)

Definition of Beta Type II Distribution

A continuous random variable $X$ is said to have a beta type II distribution with parameter $\alpha$ and $\beta$ if its p.d.f. is given by

$$ \begin{aligned} f(x) &=\frac{1}{B(\alpha,\beta)}\cdot\frac{x^{\alpha-1}}{(1+x)^{\alpha+\beta}}; x>0, \alpha, \beta > 0. \end{aligned} $$

where,

  • $B(\alpha,\beta) =\frac{\Gamma \alpha \Gamma \beta}{\Gamma (\alpha+\beta)}=\int_0^1 x^{\alpha-1}(1-x)^{\beta-1}\; dx$ is a beta function and

  • $\Gamma \alpha$ is a gamma function.

Reference

Refer step by step tutorial on Beta Type-II Distribution to understand Mean and Variance of Beta Type-II Distribution, Harmonic Mean of Beta Type-II Distribution.

Beta Type-II Distribution

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