I am working on a problem that in one step of it I need to write down the moments of the Kumaraswamy distribution as a function of its lower order moment, meaning
$$M_k = some \, terms \times M_{k-1}$$.
The moments of the Kumaraswamy distribution is defined as
$$M_k = \beta \mathbf{B} (1+\frac{k}{\alpha},\beta)$$
(According to this reference: http://www.sciencedirect.com/science/article/pii/S1572312708000282)
I tried different ways to re-write this equation in terms of lower order moments but I couldn't succeed in finding an answer for it. I appreciate if someone can help me with this. Thank you.
Best regards,
Ehsan