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Hermite and Laguerre polynomial density approximants have been utilized in order to make inference for the location and scale parameters of an exponential distribution based on K-sample Type-II censored data. First, we evaluate the exact moments of the pivots based on the Best Linear Unbiased Estimators (BLUEs) of the parameters and then, based on these moments, their density approximations are obtained using orthogonal polynomials. A comparative study of the percentiles obtained from the orthogonal polynomial approximation of the distributions of the pivots and the resulting interval estimation of the parameters to the corresponding exact numerical results of Balakrishnan and Lin (2005) and Balakrishnan et al. (2004) is carried out. A comparison is also made with the approximate inference based on the maximum likelihood estimators (MLEs) of the parameters. These comparative studies reveal that the proposed density approximant-based techniques provide very accurate inference.

Several estimators of the coefficient of an AR(1) process can be expressed as the ratio of two quadratic forms. In this article, we are considering the ordinary leastsquares, a modified least-squares, the Yule-Walker, and Burg's estimators. It will be shown that the modified least-squares estimator is the least biased and that the ordinary least-squares and Burg's estimators share very similar distributional properties. An integral representation of the moments of these estimators is provided and a methodology is proposed for correcting their bias. Bounds for the supports of the Yule-Walker and Burg's estimators are determined and the density functions of those estimators are then approximated in terms of Jacobi polynomials. Finally, confidence intervals for the autoregressive coefficient are determined from replicated series.