Topp-Leone distribution is a continuous unimodal distribution used for modeling lifetime phenomena. Topp-Leone distribution has a J-shaped density function with a hazard function of bathtub-shaped and has wide range of applications in reliability fields. This distribution has attracted recent attention for the statistician but has not been discussed in detail in Bayesian approach. This paper is concerned with the estimation of shape parameter of Topp-Leone Distribution using various Bayesian approximation techniques like normal approximation, Tierney and Kadane (T-K) Approximation. Different informative and non-informative priors are used to obtain the Baye’s estimate of parameter of Topp-Leone Distributions under different approximation techniques. A simulation study has also been conducted for comparison of Baye’s estimates obtained under different approximation using different priors.
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