# 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 VRCBuzz co-founder and passionate about making every day the greatest day of life. Raju is nerd at heart with a background in Statistics. Raju looks after overseeing day to day operations as well as focusing on strategic planning and growth of VRCBuzz products and services. Raju has more than 25 years of experience in Teaching fields. He gain energy by helping people to reach their goal and motivate to align to their passion. Raju holds a Ph.D. degree in Statistics. Raju loves to spend his leisure time on reading and implementing AI and machine learning concepts using statistical models.