Kumaraswamy Distribution Variance Calculator

For the Kumaraswamy distribution with parameters $a > 0$ and $b > 0$ , the $k$ th moment is $E [X^{k}] = b \frac{Γ (1 + \frac{k}{a}) Γ (b)}{Γ (1 + \frac{k}{a} + b)} .$ In particular, the mean is $μ = b \frac{Γ (1 + \frac{1}{a}) Γ (b)}{Γ (1 + \frac{1}{a} + b)},$ and the variance is $Var (X) = E [X^{2}] - μ^{2},$ where $E [X^{2}] = b \frac{Γ (1 + \frac{2}{a}) Γ (b)}{Γ (1 + \frac{2}{a} + b)} .$

* Enter parameters $a > 0$ and $b > 0$ . The PDF is $f (x; a, b) = a b x^{a - 1} (1 - x^{a})^{b - 1}, 0 \leq x \leq 1.$

Step 1: Enter Parameters

Parameter

a

e.g., 2

Parameter

b

e.g., 3

Related Calculators

Kumaraswamy Distribution Mean Calculator: Accurately determine the expected value or mean for given parameters.
Kumaraswamy Distribution Median Calculator: Identify the median value, which divides the distribution into two equal probability areas.
Kumaraswamy Distribution Mode Calculator: Calculate the mode, the value that appears most frequently within the distribution.
Kumaraswamy Distribution PDF Calculator: Compute the probability density function for precise likelihood evaluation.
Kumaraswamy Distribution CDF Calculator: Evaluate cumulative probabilities up to a specified point.
Kumaraswamy Distribution Inverse CDF Calculator: Determine the value corresponding to a specified cumulative probability.

Step 1: Enter Parameters

Calculated Variance

Related Calculators