Download A bias analysis of Weibull models under heaped data by Augustin T., Wolff J. PDF

By Augustin T., Wolff J.

Retrospectively accumulated period facts are usually mentioned incorrectly. an enormous kind of such an errors is heaping - respondents are likely to round-off or round-up the information in keeping with a few rule of thumb. for 2 detailed circumstances of the Weibull version we learn the behaviour of the 'naive estimators', which easily forget about the size mistakes because of heaping, and derive closed expressions for the asymptotic bias. those effects provide a proper justification of empirical proof and simulation-based findings stated within the literature. also, occasions the place a striking bias needs to be anticipated will be pointed out, and a precise bias correction will be played.

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4) denotes the inner product and δ (l − m) is the Dirac delta where , function. 5 is the first-order homogeneous functional, which means that Y1[cx(n)] = cY1[x(n)], where c is a constant. 5 can be expressed by the block diagram shown in figure 3-2: x(n) b0 a1(0) b1 a1(1) Y1[x(n)] # bm a1(m) Figure 3-2. 6, we conclude that a general first-order Volterra system with DC term is one for which the response to a linear combination of inputs is the same as the linear combination of the response of each individual input.

7) where R = S-1. 7 is the widely used form of QR decomposition. The original column in P can always be augmented with additional vector vn in such a way that matrix [P | V] has n linearly independent columns. The Gram-Schmidt procedure can then be applied to construct a full set of orthonormal vectors {qj | j = 1,…,m} which can be used to find the n× m matrix Q. Determination of a QR decomposition is not generally straightforward. There are several computer algorithms developed for this purpose.

The first difficulty concerns the measurement of Volterra kernels of a given system, because no exact method of isolating the individual Volterra operator exists. The second problem concerns the large eigenvalue spread issue which implies that slow convergence speed and large misadjustment may be expected, especially for the LMS-type adaptive algorithm. 2 Discrete Nonlinear Wiener Representation Because of these two difficulties in Volterra model representation, with proper rearrangement, a Volterra system can be described in an alternative form which is called the nonlinear Wiener model.

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