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
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