A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed method are described. In particular it is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist. Moreover it gives consistent, asymptotically efficient estimators in situations where ML fails. Examples are given including numerical ones showing the advantages of the method.

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Pisarenko method is an important technique to estimate the sinusoidal signal frequencies in white noise. In this paper, we show that the assumption of fair white noise and its corresponding equal values diagonal covariance matrix can be perturbed in some noise environments. Therefore, the simple criterion form of Pisarenko is not suitable and other modified algorithms are to be proposed to alleviate this problem. These algorithms and their results are shown.