For two constants, $a,b$ I am interested in the following integral:
$$\int_0^{b-a} \frac{k}{\lambda} \bigg(\frac{y}{\lambda}\bigg)^{k-1} \exp \bigg[-\big(\frac{y}{\lambda}\big)^k - \big(\frac{(b-y)}{\theta}\big)^l \bigg] dy$$
The first part of the integral up to the second term in the exponent is equivalent to a Weibull density with easy to derive definite integral. I am not sure if it is possible to handle the second term in the exponent in closed form. Do you have any ideas how to approach this?
