Advances and Applications in Statistics
Volume 3, Issue 1, Pages 67 - 76
(April 2003)
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A GENERALIZED GEOMETRIC DISTRIBUTION AND ITS APPLICATION
M. E. Ghitany (Kuwait) and D. K. Al-Mutairi (Kuwait)
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Abstract: In this paper we derive a
two-parameter discrete distribution, called
generalized geometric distribution, which
includes the Poisson-Lomax, geometric, and
Poisson-Lindley distributions as special cases.
Recurrence relations for calculating the
probabilities and factorial moments of the
distribution are given. For all values of the
parameters, it is shown that the distribution is
unimodal. Also, it is shown that the
distribution has a failure rate (mean residual
life) which may be decreasing, constant, or
increasing (increasing, constant, or
decreasing). Application of the proposed
distribution to real data is given and its
goodness-of-fit is demonstrated. |
Keywords and phrases: mixed Poisson distribution, factorial moments, unimodality, log-convexity, log-concavity, failure rate, mean residual life. |
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