I'm interested in estimating the shape parameters of a Kumaraswamy distribution from sample data. The closest research I can find is Jones' paper from 2009 which analyses a maximum likelihood method, but suggests only generic root-finding for computing the parameter estimates. (2018). Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring. American Journal of Mathematical and Management Sciences: Vol. 37, No. 3, pp. 243-261. Keywords Kumaraswamy distribution Maximum likelihood Maximum spacing Parameter estimation Simulation Introduction In 1980, Kumaraswamy [11] introduced a new distribution with applications in hydrology. The cumulative distribution function (cdf) of this new distribution is given by FðxÞ¼1 ðÞ1 xa b; 0\x\1; ð1Þ where a[0 and b[0. Jones [10] discussed properties of the Kumaraswamy Kumaraswamy( 1980)proposedatwo-parameterdistributionsupportedon (0,1) with probabilitydensityfunctiongivenby, f X(x;α,β)= αβxα−1(1−xα)(β−1), 0≤ x ≤ 1, (1) (2018). Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring. American Journal of Mathematical and Management Sciences: Vol. 37, No. 3, pp. 243-261. This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. We have considered estimation of the parameters of the Kumaraswamy distribution using ten methods, namely, maximum likelihood estimation, moments estimation, L-moments estimation, percentile estimation, least squares estimation, weighted least squares estimation, maximum product of spacings estimation, Cramér–von Mises estimation, Anderson–Darling estimation and right-tailed Anderson–Darling estimation. It is not feasible to compare these methods theoretically. We have performed an
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