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We develop a risk-efficient sequential procedure for estimatingthe parameter θ of the uniform density on (0,θ). We give explicit expressions for the distribution of the stoppingtime and derive its expectation and variance. We also tabulate thevalues of the expected stopping time and its standard deviationfor some selected values of the parameter. Asymptotic propertiessuch as efficiency and risk-efficiency are established

Sequential risk-efficient estimation of the parameter in the uniform density