<p>According to Bhattacharya (Metrika 11:133–144, 1967) it is known that a lifetime distribution can be generated from the well-known exponential distribution by assuming that the rate parameter is a random variable with probability density function of the beta distribution. The resulting distribution will have a probability density function which can be expressed in term of the Whittaker function of the second kind or in term of the Tricomi hypergeometric function. In this paper our aim is to show the infinite divisibility of the above mentioned Whittaker lifetime distribution considered by Bhattacharya. We prove that the Whittaker distribution in question belongs to the class of hyperbolically completely monotone densities, generalized gamma convolutions, self-decomposable distributions and consequently it is infinitely divisible. Moreover, we show that the survival function of the above mentioned distribution is in fact the Laplace transform of another infinitely divisible distribution, which belongs also to the class of hyperbolically completely monotone densities, generalized gamma convolutions, self-decomposable distributions. Finally, we show some similar results for a Whittaker distribution related to the inverted beta distribution and considered by Fitzgerald (Stoch Environ Res Risk Assess 14:139–158, 2000).</p>