The likelihood is proportional to θ⁻¹⁵ subject to θ≥max x_i,and decreases with θ. The usual endpoint MLE is θ̂=7. The CDF is (x/θ)³,so the 1/8 quantile is θ/2. Its invariant estimate is **3.5**. With literally open support x<θ,the likelihood supremum is approached at 7 from above;the standard equivalent density convention includes the endpoint.
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