L-moment ratio diagrams are increasingly being used in the literature for selecting a probability distribution function for regional frequency analysis. Two graphical methods are often used in the distribution selection process, the sample average and a line of best-fit through the sample L-moment ratios. Examples of homogeneous and heterogeneous regional samples are simulated to illustrate the...

Here ∑∗ denotes summation over primitive characters χ (mod q), φ(q) denotes the number of primitive characters (mod q), and ω(q) denotes the number of distinct prime factors of q. Note that φ(q) is a multiplicative function given by φ(p) = p − 2 for primes p, and φ(p) = p(1 − 1/p) for k ≥ 2 (see Lemma 1 below). Also note that when q ≡ 2 (mod 4) there are no primitive characters (mod q), and so ...

Fragility curves represent the probabilities that structural damages, under various levels of seismic excitation, will exceed the specified damage states by means of earthquake intensity damage relations. Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for the seismic evaluati...

Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein’s operator. Hosking (1990, 1992) proposes the concept of L-moment which better summarizes the characteristics of a distribution than conventio...

for certain explicitly computable constants ai. The difficult part of extending Ingham’s result to include the lower-order terms is asymptotically evaluating the off-diagonal terms. The family of all primitive Dirichlet L-functions of modulus q is similar in some ways to the Riemann zeta function in t-aspect, but is more difficult to analyze. In 1981, Heath-Brown obtained an asymptotic formula ...

Moment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters, this will provide semiparametric estimates or tests. If we use the score to construct moment restrictions to e...

A transparent argument is used to study the structure of the set of numbers representable as ax + by, with x, y ≥ 0. Moment sums of representable numbers are evaluated in terms of Bernoulli numbers.

for any value of x in the interval (a, b). Chebyshev motivated his problem by investigation of limit theorems in probability theory, with some related work done even earlier by Heine. It was completely resolved by Markov; for more detailed comments and description of the related developments see Shohat and Tamarkin (1943), Akhiezer (1965) and Gautschi (1981). Here we will not describe the well ...