Lifetime Data Anal (2010) 16:431–447 DOI 10.1007/s10985-009-9142-4 A new method for interval estimation of the mean of the Gamma distribution H. V. Kulkarni · S. K. Powar Received: 18 October 2008 / Accepted: 6 November 2009 / Published online: 25 November 2009 © Springer Science+Business Media, LLC 2009 Abstract The two parameter Gamma distribution is widely used for modeling life- time distributions in reliability theory. There is much literature on the inference on the individual parameters of the Gamma distribution, namely the shape parameter k and the scale parameter θ when the other parameter is known. However, usually the reliability professionals have a major interest in making statistical inference about the mean lifetime μ, which equals the product θ k for the Gamma distribution. The problem of inference on the mean μ when both parameters θ and k are unknown has been less attended in the literature for the Gamma distribution. In this paper we review the existing methods for interval estimation of μ. A comparative study in this paper indicates that the existing methods are either too approximate and yield less reliable confidence intervals or are computationally quite complicated and need ad- vanced computing facilities. We propose a new simple method for interval estimation of the Gamma mean and compare its performance with the existing methods. The comparative study showed that the newly proposed computationally simple optimum power normal approximation method works best even for small sample sizes. Keywords Interval estimation · Gamma mean · Comparative study · Optimum power normal approximation transformation H. V. Kulkarni (B ) · S. K. Powar Department of Statistics, Shivaji University, Kolhapur, India e-mail: kulkarnih1@rediffmail.com S. K. Powar e-mail: sarjerao.powar@rediffmail.com 123