A Comparative study between Riemann-Stieltjes and Lebesgue-Stieltjes Integration using Discrete Distribution Functions

2020 ◽  
Author(s):  
Gane Samb Lo ◽  
Aladji Babacar Niang ◽  
Cherif Mamadou Moctar Traore
Keyword(s):  
Comparative Study ◽  
Discrete Distribution ◽  
Distribution Functions ◽  
Stieltjes Integration

Discrete Distribution Functions for Log-Normal Moments

2020 ◽  
pp. 1-21
Author(s):  
Catherine M. Bonan-Hamada ◽  
William B. Jones ◽  
W. J. Thron ◽  
Arne Magnus
Keyword(s):  
Discrete Distribution ◽  
Distribution Functions ◽  
Log Normal

scholarly journals Size, Shape, and Internal Atomic Ordering of Nanocrystals by Atomic Pair Distribution Functions: A Comparative Study of γ-Fe2O3Nanosized Spheres and Tetrapods

2009 ◽  
Vol 131 (40) ◽  
pp. 14264-14266 ◽  
Author(s):  
Valeri Petkov ◽  
P. Davide Cozzoli ◽  
Raffaella Buonsanti ◽  
Roberto Cingolani ◽  
Yang Ren
Keyword(s):  
Comparative Study ◽  
Distribution Functions ◽  
Atomic Ordering ◽  
Atomic Pair ◽  
Pair Distribution Functions

scholarly journals On convergence and compactness in variation with shift of discrete probability laws

2021 ◽  
Vol 8 (3) ◽  
pp. 385-393
Author(s):  
Ivan A. Alexeev ◽  
◽  
Alexey A. Khartov ◽  
Keyword(s):  
Real Line ◽  
Discrete Distribution ◽  
Distribution Functions ◽  
Divisible Distribution ◽  
Characteristic Functions ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
The Real ◽  
Convergence In Variation ◽  
Compactness Theorems

We consider a class of discrete distribution functions, whose characteristic functions are separated from zero, i. e. their absolute values are greater than positive constant on the real line. The class is rather wide, because it contains discrete infinitely divisible distribution functions, functions of lattice distributions, whose characteristic functions have no zeroes on the real line, and also distribution functions with a jump greater than 1/2. Recently the authors showed that characteristic functions of elements of this class admit the Lévy-Khinchine type representations with non-monotonic spectral function. Thus our class is included in the set of so called quasi-infinitely divisible distribution functions. Using these representation the authors also obtained limit and compactness theorems with convergence in variation for the sequences from this class. This note is devoted to similar results concerning convergence and compactness but with weakened convergence in variation. Replacing of type of convergence notably expands applicability of the results.

scholarly journals A nonparametric approach toward upper bounds to transit time distribution functions

2017 ◽  
Author(s):  
Earl Bardsley
Keyword(s):  
Distribution Function ◽  
Transit Time ◽  
Time Distribution ◽  
Discrete Distribution ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Linear Measure ◽  
Time Varying ◽  
Transit Time Distribution ◽  
The Individual

Abstract. A nonparametric method is proposed as a possible approach to obtaining upper bounds to distribution functions of time-varying transit times for catchment environmental tracers. A discretization is employed for the tracer throughput process, with tracer input represented as a sequence of K discrete pulses over a given time period. Each input pulse is associated with a different and unknown upper-bounded nonparametric discrete transit time distribution. The model transit time distribution function is therefore a K-component finite mixture of different and unknown discrete distribution functions, weighted by the relative magnitudes of the respective tracer pulses. Upper bounds to this distribution function can be obtained by linear programming to achieve a sequence of K discrete optimised transit time distributions which yield the maximum possible value of tracer fraction less than a given age, subject to a constraint of matching the catchment tracer output time series to some specified linear measure of accuracy. The individual optimised distributions do not estimate actual transit time distributions and the optimisation procedure is not hydrological modelling. This is actually a strength of the methodology in that the true transit time distributions are permitted to be created as a consequence of any time-varying nonlinear catchment process with complete or partial mixing. However, a negative aspect is that the extreme flexibility of K different nonparametric distributions is likely to give transit time distribution functions upper bounds near 1, unless sufficient constraints can be imposed on the form of the individual optimised distributions. There is a possibility, however, that optimising just a single nonparametric L-shaped discrete distribution could yield useful distribution function upper bounds for time-varying situations.

Sign in / Sign up

Export Citation Format

Share Document