ABSTRACT Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they do not investigated its moments and the order statistics. In this paper the BF density function and the density function of the order sta...

Many familiar and useful spaces of continuous or differentiable functions are Hilbert or Banach spaces, with pleasant completeness properties, but many are not. Some are Fréchet spaces, thus still complete, but lacking some of the conveniences of Banach spaces. Some other important spaces are not Fréchet, either. Still, some of these important spaces are colimits of Fréchet spaces (or of Banach...

We introduce the discrete Fréchet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of similarity than the discrete Fréchet distance (and its variants), since the latter measure is indifferent to (matched) pairs of points that are relatively close...

1. Fréchet space C∞[a, b] 2. Fréchet space of smooth functions E = C∞(Rn) 3. Fréchet space of Schwartz functions S on R 4. LF-space of test functions D on R 5. Generalized functions (distributions) D∗, S ∗, E∗ as linear functionals 6. Generalized functions D∗, S ∗, E∗ as completions of D 7. Fourier transforms of tempered distributions 8. Distributions supported at a point 9. Appendix: weak dual...

The Fréchet distance between two curves in a metric space is a measure of the similarity between the curves. We present a discrete variation of this measure. It provides good approximations of the continuous measure and can be efficiently computed using a simple algorithm. We also consider variants of discrete Fréchet distance, and find an interesting connection to measuring distance between th...

In this paper we show that the so-called array Fréchet problem in Probability/Statistics is (max,+)-linear. The upper bound of Fréchet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Fréchet problem and the Monge property of bivari...

The Fréchet distance is a well-known metric to measure similarity of polygonal curves. In the first part of this thesis, we introduce a new metric called Fréchet distance with speed limits and provide efficient algorithms for computing it. The classical Fréchet distance between two curves corresponds to the maximum distance between two point objects that traverse the curves with arbitrary non-n...

We construct two counter-examples related to Fréchet differentiability in infinite dimensions. The first one gives a convex Lipschitzian function on a Banach space such that its convolution with a given measure is Fréchet differentiable only on a measure zero set. The second one gives a Borel function on a space with a Gaussian measure such that it is Lipschitzian along the Cameron–Martin subsp...