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In this paper, we introduce a generalization of the Kantorovich-type Bernstein operators based on q-integers and get a Bohman-Korovkin-type approximation theorem of these operators. We also compute the rate of convergence using the first modulus of smoothness. [ABSTRACT FROM AUTHOR]

This article is an expository paper to demonstrate the usefulness of Pearson curves in density estimation especially for those unaware of this early development in statistics. It is shown how to fit the curves and how very good approximate percentage points can be obtained for intractable distributions when the first four moments (or three moments and one endpoint) are known exactly (not estimated from sample data). The effectiveness of this method in density estimation is illustrated in three somewhat disparate contexts and reference is given to others. In general, the Pearson curves give an excellent approximation to the long tail of a distribution, the tail-most often needed in practical work. [ABSTRACT FROM AUTHOR]

This paper investigates the distribution-free outer confidence interval for the quantile interval introduced by Wilks. Besides exact expressions and a recurrence formula some bounds are derived for the probability of correct coverage of the quantile interval which improve bounds known up to now, and which are tested in several examples. Asymptotic approximations are discussed and applications of the developed methods to other statistics based on order statistics are indicated. [ABSTRACT FROM AUTHOR]

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's "precise measurement" is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous distributions with high local concentrations of density, Mixed-type distributions constructed from the natural conjugate prior distributions are proposed and illustrated in the normal-sampling case for unified Bayesian inference in testing and estimation contexts. [ABSTRACT FROM AUTHOR]

In their paper, Good and Gaskins determine empirically the number of terms required in Hermite and Fourier expansions to obtain equivalent degrees of approximation. The argument that a sign pattern in the coefficients in the Hermite expansion of a function slows the convergence is ingenious, but there is another reason for the better approximation by Fourier series than for Hermite series that is probably more important.