This paper deals with the estimation of the stress-strength reliability parameter R ¼ PðY\XÞ, when X and Y are independent random variables, where X and Y have inverted gamma distribution. The maximum likelihood estimator and the approximate maximum likelihood estimator of R are obtained. The Bayesian estimation of the reliability parameter has been also discussed under the assumption of independent gamma prior, squared error loss and Linex error loss functions. Finally, two real data applications are given for showing the flexibility and potentiality of the inverted gamma distribution.

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